17

IAOe?IIAEUeIA AEAAeAI?ss IAOE OEPA?IE

?INOEOOO O?CEEE EIIAeAINIAAIEO NENOAI

Ia i?aaao ?oeiieno

AA?OIEssE Oa?an Ieoaeeiae/

OAeE 538.955-405

AIEEA AACEAAeO OA ACA?IIAe?E ??CIEO OEI?A

IA OA?IIAeEIAI?*I? OA AeEIAI?*I? AEANOEAINO?

IIAeAEUeIEO NI?IIAEO NENOAI

01.04.02 – oai?aoe/ia o?ceea

A A O I ? A O A ? A O

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

EUeA?A – 1999Aeena?oaoe??th ? ?oeiien

?iaioo aeeiiaii a ?inoeooo? o?ceee eiiaeainiaaieo nenoai Iaoe?iiaeueii?
aeaaeai?? iaoe Oe?a?ie.

Iaoeiaee ea??aiee–aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Eaaeoeueeee
?iiai ?iiaiiae/, ?inoeooo o?ceee eiiaeainiaaieo nenoai IAI Oe?a?ie,
i.Euea?a, caa?aeoaa/ a?aeae?eo oai??? iiaeaeueieo ni?iiaeo nenoai

Io?oe?ei? iiiiaioe–

–aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Oea/ Ieeiea Aaneeueiae/,
*a?i?aaoeueeee aea?aeaaiee oi?aa?neoao, i.*a?i?aoe?, caa?aeoaa/ eaoaae?e
oai?aoe/ii? o?ceee

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, noa?oee iaoeiaee ni?a?ia?oiee Aieiaa/
TH??e Aaneeueiae/, ?inoeooo o?ceee eiiaeainiaaieo nenoai IAI Oe?a?ie,
i.Euea?a, noa?oee iaoeiaee ni?a?ia?oiee.

I?ia?aeia i?aai?caoe?y–?inoeooo oai?aoe/ii? o?ceee ?i. I.I.Aiaiethaiaa
IAI Oe?a?ie, a?aeae?e iaoaiaoe/iiai iiaeaethaaiiy, i.Ee?a

Caoeno a?aeaoaeaoueny “23” aa?aniy 1999 ?ieo i “1530”’ ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 35.156.01 i?e ?inoeooo? o?ceee
eiiaeainiaaieo nenoai Iaoe?iiaeueii? aeaaeai?? iaoe Oe?a?ie ca
aae?anith: 290011 i. Euea?a, aoe.Na?ioe?oeueeiai, 1.

C aeena?oaoe??th iiaeia iciaeiieoenue o iaoeia?e a?ae?ioaoe? ?inoeoooo
o?ceee eiiaeainiaaieo nenoai IAI Oe?a?ie ca aae?anith: 290026 i.Euea?a,
aoe.Eicaeueieoeueea, 4.

Aaoi?aoa?ao ?ic?neaii “21” na?iiy 1999 ?ieo.

A/aiee nae?aoa?niaoe?ae?ciaaii? a/aii? ?aaee Ae 35.156.01,eaiaeeaeao
o?c.-iao. iaoe O.?.E?ioiaeuenueeee

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Ni?iia? iiaeae? oe?iei aeei?enoiaothoueny aeey
iieno naaiaoiaeaeo?e/ieo oa iaai?oieo iaoa??ae?a, a yeeo iiaeia
aeae?eeoe aeene?aoi? noaie, ui eieae?ciaai? ia aoceao. I?e oeueiio
o?ce/i? aeanoeaino? oaeeo nenoai iiaeooue ??cei i?iyoeny ?c ci?iith
aca?iiae?? /e ii?ooaiiyi iaeii??aeiino? a nenoai?. Cie?aia, a?aooaaiiy
aioeneiao?e/ii? aca?iiae?? Aecyeioeinueeiai-Ii??y o eaaioiaeo ni?iiaeo
nenoaiao i?eaiaeeoue aei aeieeiaiiy iani?ai??ii? oace, a ci?ia ?aae?ona
ae?? iai?iii? aca?iiae?? iiaea i?eaanoe aei ci?ie oa?aeoa?o iiaaae?iee
no?oeoo?iiai oaeoi?a iiaeae?. Caaea/a nooo?ai oneeaaeith?oueny i?e
?icaeyae? aeiaaeeiaeo iaiaeii??aeiinoae, ye? iiaeaeththoueny aeiaaeeiaei
?iciiae?eii cia/aiue ia?aiao??a aai?eueoii?aia. Ine?eueee /enei oi/ieo
?acoeueoao?a aeey iaaii?yaeeiaaieo nenoai ? iaaaeeeei, eiaeia iiaa
iiaeaeue, o?ce/i? oa?aeoa?enoeee yei? iiaeia io?eiaoe aac aeei?enoaiiy
iaaeeaeaiue, i?noeoue aaaeeeao ?ioi?iaoe?th i?i niaoeeo?/i? aeanoeaino?
iaaii?yaeeiaaieo nenoai.

A aeai?e aeena?oaoe?ei?e ?iaio? ?icaeyaea?oueny iaeiiaei??ia ?cio?iiia
ni?i-1/2 XY iiaeaeue ?c aca?iiae??th Aecyeioeinueeiai-Ii??y o
aeiaaeeiaiio ei?aioeiaiio iiia?a/iiio iie? oa io?eiothoueny oi/i?
?acoeueoaoe aeey ?? oa?iiaeeiai?/ieo ooieoe?e. Oi?ioeth?oueny /eneiaee
iaoiae, ui aeicaiey? aea/eoe aeanoeaino? iaecaaaeuei?oeo ni?i-1/2
ai?cio?iiieo XY eaioethaee?a ne?i/aiiiai ?ici??o c aeia?eueiei oeiii
iaaii?yaeeiaaiino?. Iaaii?yaeeiaaia aeaieiiiiiaioia iiaeaeue ?c?i?a c
??aiiaaaeiei oeiii aaceaaeo ?icaeyaea?oueny a iaoiae? ?icaeiaiue ca
iaa?iaiei ?aae?onii aca?iiae??. C ?ioiai aieo, a ?aieao iaoiaeo
aoaeoeaiiai iiey aeyniaii aieea oeio aca?iiae?? ia oa?aeoa?enoeee
iiaeae? ?c?i?a.

Aeena?oaoe?eio ?iaioo aeeiiaii a ?inoeooo? o?ceee eiiaeainiaaieo nenoai
IAI Oe?a?ie ca?aeii c ieaiaie ?ia?o ca oaiaie: oeo? 1.4.8.12 ?
0194022989 “Aeine?aeaeaiiy iaiaeii??aeieo oa iaaii?yaeeiaaieo
aeaeo?iiieo inaaaeini?iiaeo nenoai iaoiaeii eiii’thoa?iiai
iiaeaethaaiiy”; oeo? 1.4.8.11 ? 0194022990 “?ic?iaea i?e?ineii?/ii?
oai??? ?aeaenaoe?eieo yaeu ? oa?iiaeeiai?/ieo aeanoeainoae
iaaii?yaeeiaaieo nenoai o eeanoa?iiio i?aeoiae?”.

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith ?iaioe ? oai?aoe/iee iien
iiaeaeueieo ni?iiaeo nenoai c aeiaaeeiaith iaiaeii??aei?noth oa ??cieie
aca?iiae?yie, a naia:

· io?eiaiiy oi/ieo ?acoeueoao?a aeey ?aeaae?ciaaieo aeiaaeeiaeo
iaeiiaei??ieo ni?i-1/2 iiaeaeae ?c aca?iiae??th i?ae iaeaeeae/eie
non?aeaie;

· oi?ioethaaiiy iaoiaeo ?iceeaae?a ca iaa?iaiei ?aae?onii aca?iiae??
aeey ??aiiaaaeii iaaii?yaeeiaaii? iiaeae? ?c?i?a c aaceniei a?aooaaiiyi
ei?ioeinyaeieo aca?iiae?e;

· iioe?aiiy iaoiaeo aoaeoeaiiai iiey ia iiaeaeue ?c?i?a c aeia?eueiith
aca?iiae??th oa aeine?aeaeaiiy aieeao aca?iiae?e ??cieo oei?a ia
iiaaae?ieo oa?iiaeeiai?/ieo oa aeeiai?/ieo oa?aeoa?enoee nenoaie.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a: A aeena?oaoe?ei?e ?iaio?
aia?oa io?eiaii oi/i? ?acoeueoaoe aeey oa?iiaeeiai?/ieo ooieoe?e
iaaii?yaeeiaaiiai ?cio?iiiiai ni?i-1/2 XY eaioethaeea ?c aca?iiae??th
Aecyeioeinueeiai-Ii??y o aeiaaeeiaiio ei?aioeiaiio iiia?a/iiio iie?.
Y?oiooth/enue ia io?eiaieo oi/ieo ?acoeueoaoao, c’yniaaii iaae?
canoiniaiino? iaaeeaeaiiy eiiooaoe?eieo ni?aa?aeiioaiue Aica,
iaaeeaeaiiy Oyae?eiaa oa iaaeeaeaiiy eiaa?aioiiai iioaioe?aeo.

Cai?iiiiiaaii /eneiaee iaoiae aeine?aeaeaiiy iaaii?yaeeiaaii?
ocaaaeueiaii? iaeiiaei??ii? ni?i-1/2 XY iiaeae? o iiia?a/iiio iie?.
?ic?aoiaaii iiia?a/io aeeiai?/io ni?eeiyoeea?noue iaeiiaei??ii? iiaeae?
?c?i?a c aca?iiae??th Aecyeioeinueeiai-Ii??y o aeiaaeeiaiio iiia?a/iiio
iie?. Aeaoaeueii aea/aii oa?iiaeeiai?/i? oa ei?aeyoe?ei? ooieoe??
iaeiiaei??ii? iiaeae? ?c?i?a o aeiaaeeiio iiia?a/iiio iie?.

Cai?iiiiiaaii aaceniee i?aeo?ae c a?aooaaiiyi ei?ioeinyaeieo oa
aeaeaeinyaeieo aca?iiae?e aeey aeaieiiiiiaioii? iaaii?yaeeiaaii? iiaeae?
?c?i?a.

Cae?eniaii ocaaaeueiaiiy iaoiaeo aoaeoeaiiai iiey ia aeiaaeie iiaeae?
?c?i?a c aeia?eueiith aca?iiae??th. ?ic?aoiaaii o?ce/i? oa?aeoa?enoeee
iiaeae? c ??cieie aca?iiae?yie, ia/eneaii ooieoe?th ?iciiae?eo
eieaeueieo iie?a oa anoaiiaeaii, ye aeieea? ne?i/aiia oe?eia e?i?e o i?e
?c aca?iiae??th i?ae an?ia ni?iaie.

I?aeoe/ia ? iaoeiaa cia/aiiy iaea?aeaieo ?acoeueoao?a. Io?eiai? a ?iaio?
oi/i? ?acoeueoaoe aeicaieythoue anoaiiaeoe iaae? canoiniaiino?
iaaeeaeaiiy eiiooaoe?eieo ni?aa?aeiioaiue Aica, iaaeeaeaiiy oeio
Oyae?eiaa oa iaaeeaeaiiy eiaa?aioiiai iioaioe?aeo aeey iiaeaeae c
ae?aaiiaeueiei aaceaaeii. *eneia? ?acoeueoaoe io?eiai? aeey
iaeiiaei??ii? iiaeae? ?c?i?a o aeiaaeeiaiio iiia?a/iiio iie? aeyaeee
niaoeeo?/i? iniaeeaino? iiaaae?iee oeeo nenoai. Cie?aia, o aeai?e
iiaeae? i?e iaaieo oiiaao aeieeathoue aeaiaioa?i? caoaeaeaiiy c
aeecueeeie aei ioey aia?a?yie, ui i?eaiaeeoue aei ci?ie
iecueeioaiia?aoo?iiai oiaeo oaiei?iiino?. E??i oiai, zz-ei?aeyoe?eia
aeiaaeeia oeeo nenoai c?inoa? i?e neaaiio aeeth/aii? a nenoaio
aeiaaeeiai? iaiaeii??aeiino?.

Cai?iiiiiaaiee iaoiae ?iceeaaeo ca iaa?iaiei ?aae?onii aeaeaeinyaeii?
aca?iiae?? i?e iaeii/aniiio aaceniiio a?aooaaii? ei?ioeinyaeieo
ei?aeyoe?e aeey aeaieiiiiiaioii? iaaii?yaeeiaaii? iiaeae? ?c?i?a
aeicaiey? cae?enieoe ei?aeoiee iien iaio oei?a ei?aeyoe?e aeey ?aaeueieo
nenoai. Cie?aia, oeth oai??th iiaeia canoinoaaoe aeey iieno
eaac?iaeiiaei??ieo iaaii?yaeeiaaieo naaiaoiaeaeo?ee?a c aiaeiaaeie
ca’yceaie.

Iaoiae aoaeoeaiiai iiey canoiniaaiee aei iiaeae? ?c?i?a c aeia?eueiith
aca?iiae??th, ui aeicaiey? io?eiaoe ne?i/aiio oe?eio e?i?e iiaeeiaiiy
iaai?oiiai ?aciiaino, yea aeieea? a ?aaeueieo nenoaiao aiane?aeie
aeaeaeinyaeiiai oa?aeoa?o i?aeaoceiaeo aca?iiae?e.

Iniaenoee aianie caeiaoaa/a. O ni?eueieo ioae?eaoe?yo aaoi?ia?
iaeaaeaoue ocaaaeueiaiiy iiaeae? I?o?ii?? (Nishimori H., Phys.Lett.A,
1984, 100, 239-243) ia aeiaaeie iayaiino? aca?iiae??
Aecyeioeinueeiai-Ii??y ? iaaiai?aiiy ?acoeueoao?a ii??aiyiiy iaaeeaeaieo
iaoiae?a c oi/ieie ?acoeueoaoaie. Aaoi? a?aa aaciina?aaeith o/anoue o
?ic?iaoe? /eneiaiai iaoiaeo aeey ocaaaeueiaii? iaeiiaei??ii? ni?i-1/2 XY
iiaeae? oa o ?ic?iaoe? iaoiaeo ?icaeiaiue ca iaa?iaiei ?aae?onii
aca?iiae?? c aaceniei a?aooaaiiyi ei?ioeinyaeieo aca?iiae?e aeey
iaaii?yaeeiaaieo ?c?i?iaeo nenoai. Aaoi?ii oaeiae i?iaaaeaii aiae?c
?acoeueoao?a ?ic?aooieo oa?iiaeeiai?/ieo oa noaoe/ieo ni?iiaeo
ei?aeyoe?eieo ooieoe?e iaeiiaei??ii? iiaeae? ?c?i?a o iiia?a/iiio iie?.
Aaoi? a?aa o/anoue o ?iaio? iaae ocaaaeueiaiiyi iaoiaeo aoaeoeaiiai iiey
aeey iiaeae? ?c?i?a c aeia?eueiith aca?iiae??th. Iaaiai?aiiy oa
?ioa?i?aoaoe?y io?eiaieo ?acoeueoao?a i?iaaaeaia ?acii ?c ni?aaaoi?aie.

Ai?iaaoe?y ?iaioe. Iniiai? ?acoeueoaoe aeena?oaoe?? aeiiia?aeaeenue ?
iaaiai?thaaeenue ia oaeeo eiioa?aioe?yo: I?aeia?iaeia eiioa?aioe?y,
i?enay/aia 150-??//th a?ae aeiy ia?iaeaeaiiy ?.Ioethy (Euea?a, 1995 ?.),
I?aeia?iaeia ?iai/a ia?aaea “Noaoenoe/ia o?ceea oa oai??y
eiiaeainiaaiiai noaio” (Euea?a, 1995 ?.), 9-oa i?aeia?iaeia eiioa?aioe?y
c oaeaeeicaaa?oiaaieo oa iaoanoaa?eueieo iaoa??ae?a (A?aoeneaaa,
Neiaa//eia, 1996 ?.), E?oiy oeiea c neeueiiei?aeueiaaieo aeaeo?iiieo
nenoai (Aeaa?aoeai, Oai?ueia, 1996 ?.), Iaoeiaee nai?ia? c noaoenoe/ii?
oai??? eiiaeainiaaieo nenoai (Euea?a, 1997 ?.), I?aeia?iaeia
eiioa?aioe?y nooaeaio?a-o?cee?a (A?aeaiue, Aano??y, 1997 ?.),
I?aeia?iaeiee nai?ia? “Oacia? ia?aoiaee oa e?eoe/i? yaeua” (Iiciaiue,
Iieueua, 1997 ?.), I?aeia?iaeia ?iai/a ia?aaea c o?ceee eiiaeainiaaieo
nenoai INTAS-Oe?a?ia (Euea?a, 1998 ?.), a oaeiae ia nai?ia?ao ?inoeoooo
o?ceee eiiaeainiaaieo nenoai Iaoe?iiaeueii? aeaaeai?? iaoe Oe?a?ie oa
a?aeae?eo oai??? iiaeaeueieo ni?iiaeo nenoai oeueiai ?inoeoooo.

Ioae?eaoe??. Ca iaoa??aeaie aeena?oaoe?? iioae?eiaaii 21 ?iaioo, a oiio
/ene? 7 noaoae a iaoeiaeo aeo?iaeao, 6 i?ai?eio?a oa 8 oac eiioa?aioe?e.
Ia?ae?e iniiaieo ioae?eaoe?e iiaeaii a e?ioe? aaoi?aoa?aoo.

No?oeoo?a oa ia’?i aeena?oaoe??. Aeena?oaoe?eia ?iaioa neeaaea?oueny ?c
anooio, i’youeio ?icae?e?a, aeniiae?a, nieneo aeei?enoaieo aeaea?ae;
eiaeai ?icae?e aeena?oaoe?? ii/eia?oueny ?c anooio oa caaa?oo?oueny
aeniiaeaie. ?iaioa aeeeaaeaia ia 133 noi??ieao (?acii c e?oa?aoo?ith —
149 noi??iie), aeeth/a? a?ae?ia?ao?/iee nienie, ui i?noeoue 160
iaeiaioaaiue o a?o/eciyieo oa caei?aeiiieo aeaeaiiyo.

CI?NO ?IAIOE

O anooi? iaa?oioiaaii aeooaeuei?noue aeine?aeaeaiue, aeeeaaeaieo o
aeena?oaoe??, noi?ioeueiaaii iaoo ?iaioe, a?aecia/aii ?? iaoeiao
iiaecio.

O ia?oiio ?icae?e? iiaeaii ei?ioeee iaeyae iniiaieo iaoiae?a
aeine?aeaeaiiy ni?iiaeo nenoai oa ?icaeyiooi i?iaeaie, ye? aeieeathoue
i?e ?icaeyae? iaaii?yaeeiaaieo nenoai, i?eaaaeaii iaeyae ioae?eaoe?e, ui
a?aeiia?aeathoue oai? aeena?oaoe??.

Ae?oaee ?icae?e iaceaa?oueny “Iaeiiaei??ia ?cio?iiia ni?i-1/2 XY
iiaeaeue c aca?iiae??th Aecyeioeinueeiai-Ii??y o aeiaaeeiaiio
ei?aioeiaiio iiia?a/iiio iie?”. O anooi? aei ?icae?eo iiaeaii ei?ioeee
iaeyae a?aeiieo oi/ieo ?acoeueoao?a aeey iaaii?yaeeiaaieo eaaioiaeo
iiaeaeae oa iaeyae iniiaieo ?ia?o, ui noinothoueny i?e?iaee aca?iiae??
Aecyeioeinueeiai-Ii??y oa aoaeo?a, ye? aiia ni?e/eiy? a iaeii??aeiiio
?cio?iiiiio ni?i-1/2 XY eaioethaeeo.

?icaeyaea?oueny eaioethaeie N ni?i?a s=1/2 c ?cio?iiiith XY aca?iiae??th
? aca?iiae??th Aecyeioeinueeiai-Ii??y i?ae iaeaeeae/eie non?aeaie o
iiia?a/iiio iie? c aeiaaeeiaith neeaaeiaith, ?iciiae?eaiith ca caeiiii
Ei?aioea. Aai?eueoii?ai iiaeae? ia? oaeee aeaeyae:

wmetafile8? ??`???????????
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A@*???&??yyyy?????Ayyy?yyy?*??o?? ???&?
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— aeiaaeeiaa ceeaaeiaa iiia?a/iiai iiey, ui caaea?oueny ei?aioeiaei
?iciiae?eii ?iia??iino?, oeaio?iaaiei iaaeiei ioey c oe?eiith . I?ney
ia?aoai?aiiy Ei?aeaia-A??ia?a i?eoiaeeii aei aai?eueoii?aia o aeaeyae?
eaaae?aoe/ii? oi?ie ca oa?i?-iia?aoi?aie, a yeiio ia a?aei?io a?ae
a?aeiii? caaea/? Eeieaea (Lloyd P. J.Phys.C, 1969, 2, 1717-1725)
eiao?oe??ioe ? eiiieaenieie.

Aeey aeine?aeaeaiiy oa?iiaeeiai?ee iiaeae? c aai?eueoii?aiii (1)
aeei?enoiao?oueny oi?iae?ci ooieoe?e Y??ia ? ?icaeyaeathoueny cai?ciaia
oa aeia?aaeia oaiia?aoo?i? aeai/ania? ooieoe?? Y??ia, icia/ai? ye

wmetafile8? ??U???????????
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ona?aaeiaio ooieoe?th Y??ia wmetafile8? ??&???????????
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ia?aoai?aiee aai?eueoii?ai iieno? nenoaio iaaca?iiae?th/eo aacni?iiaeo
oa?i?ii?a, ??aiyiiy ?ooo aeey wmetafile8? ??&???????????
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yea aeei?enoiao?oueny aeey aeine?aeaeaiiy oa?iiaeeiai?/ieo aeanoeainoae
iiaeae? (1). An? oa?iiaeeiai?/i? oa?aeoa?enoeee iaaii?yaeeiaaii? nenoaie
iiaeia ae?aceoe /a?ac ?ioa??ae a?ae u?eueiino? aeaiaioa?ieo caoaeaeaiue
wmetafile8? ??o????????????
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A ?iaio? i?iaaaeaii /eneiaee aiae?c u?eueiino? aeaiaioa?ieo caoaeaeaiue,
iiia?a/ii? iaiaai?/aiino?, noaoe/ii? ni?eeiyoeeaino? i?e ??cieo
cia/aiiiyo ia?aiao?a D. Iieacaii, ui aca?iiae?y Aecyeioeinueeiai-Ii??y
i?eaiaeeoue aei ia?aii?ioaaiiy cae/aeii? ?cio?iiii? aca?iiae??

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?MathType??0????u?th??????

a aeiaaeeiaa ei?aioeiaa iiea — aei cieeiaiiy eaaioiaiai oaciaiai
ia?aoiaeo, yeee ?nio? aeey oe??? iiaeae? i?e T=0.

Canoiniaaia aei iiaeae? iaaeeaeaiiy eiiooaoe?eieo ni?aa?aeiioaiue Aica
aeey iia?aoi??a Iaoe? wmetafile8? ?????????????
???????????yyy????.????1?????? ???????
 ????&??yyyy?????Ayyy¬yyy@??L?? ???&?
?MathType??p????u?th??????

wmetafile8? ??^???????????
???????????yyy????.????1?????? ???????
`????&??yyyy?????Ayyy¬yyy@?? ?? ???&?
?MathType??P????u?th??????

ca?aa?oueny c oi/iei, /a?ac ??cio noaoenoeeo oeae iaoiae aeyaey?oueny
iacanoiniaiei aeey iiaeae? c ei?aioeiaei aaceaaeii, ine?eueee iiyaa
aeaiaioa?ieo caoaeaeaiue c ye caaaiaeii aaeeeith a?ae’?iiith aia?a??th
?iaeoue nenoaio iano?eeith. ?ic?aooiie ooieoe?e Y??ia wmetafile8?
????????????? ???????????yyy????.????1??????
??????? ` ???&??yyyy?????Ayyy¬yyy`?? ?? ???&?
?MathType??P????u?th??????Ia iniia? io?eiaieo oi/ieo ?acoeueoao?a
ia?aa??aii oi/i?noue iaaeeaeaiiy eiaa?aioiiai iioaioe?aeo. ?ica’ycie
??aiyiiy Aeaeniia aeey ooieoe?? Y??ia iaaii?yaeeiaaii? iiaeae? iiaeia
cia?aceoe o aeaeyae? ?iceeaaeo ca ooieoe?yie Y??ia wmetafile8?
??0??????????? ???????????yyy????.????1??????
???????  a???&??yyyy?????oyyy¬yyyO??L?? ???&?
?MathType??p????u?y??????

wmetafile8? ??9??? ????????
?????????????yyy????.??????1?????? ???????
@ ???&??yyyy?????ayOy? ???&? ?MathType??`? ???u?th??????

Aea

wmetafile8? ??I???????????
???????????yyy????.????1?????? ??????? ``
???&??yyyy?????AyyyAyyy ?? ?? ???&? ?MathType????
???u?????????»????-?????ue???ue ???u?th??????

— t-iao?eoey iiaeae?, Wnr — aeayea iao?eoey, ui iieno?
iaaii?yaeeiaai?noue a iiaeae?, a iaoiio aeiaaeeo aiia ae?aaiiaeueia:
wmetafile8? ??????????????
???????????yyy????.????1?????? ??????? `A
???&??yyyy?????Ayyy¤yyy? ???? ???&?
?MathType??P????u?th??????

wmetafile8? ?????????????
???????????yyy????.????1?????? ??????? 
A???&??yyyy?????Ayyy·yyy???*?? ???&? ?MathType??

??aiyiiy aeey eiaa?aioiiai iioaioe?aeo caiaeeoueny aei aeaaa?e/iiai
??aiyiiy 3-ai ii?yaeeo. Aiii ?ica’yco?oueny, a eiai i?aenoaiiaea o ae?ac
aeey ooieoe?? Y??ia aeicaiey? ia/eneeoe ona?aaeiaio u?euei?noue
aeaiaioa?ieo caoaeaeaiue. Ii??aiyiiy c ?acoeueoaoaie /eneiaiai i?aeoiaeo
aeey ne?i/aiieo eaioethaee?a aeiaiaeeoue aenieo oi/i?noue iaoiaeo
eiaa?aioiiai iioaioe?aeo, oi/a a?i ? ia a?aeoai?th? oiiei? no?oeoo?e
ooieoe?? u?eueiino? aeaiaioa?ieo caoaeaeaiue, yea i?eoaiaiia oi/iei
?acoeueoaoai (?en.1).

A inoaiiueiio ia?aa?ao? ?icae?eo ?icaeyiooa iaeiiaei??ia ni?i-1/2 XXZ
iiaeaeue Aaecaiaa??a ?c aca?iiae??th Aecyeioeinueeiai-Ii??y o
aeiaaeeiaiio ei?aioeiaiio iiia?a/iiio iie?. Aiia a?aeiia?aea?
aeeth/aiith a aai?eueoii?ai (1) aeiaeaieo

wmetafile8? ??????????????
???????????yyy????.????1?????? ???????  a
???&??yyyy?????Ayyy1/2yyy  ??Y?? ???&? ?MathType??yeee i?ney
ia?aoai?aiiy Ei?aeaia-A??ia?a ii?iaeaeoaaoeia o oa?i?ii?ciaaiiio
aai?eueoii?ai? /eai, ui iieno? aca?iiae?th oa?i?ii?a

wmetafile8? ??3/4???????????
???????????yyy????.????1?????? ??????? 
A???&??yyyy?????Ayyy1/2yyy???Y?? ???&? ?MathType??

Aeey ooieoe?e Y??ia aeueo ii?yaee?a, ye? aeieeathoue o ??aiyii? ?ooo,
canoiniao?oueny iaaeeaeaiiy oeio Oa?o??-Oiea. A ?acoeueoao? ?ica’ycie
aeey iaa?aeiii? ooieoe?? Y??ia i?noeoeia iaa?aeii? na?aaei? oeio
wmetafile8? ?????????????
???????????yyy????.????1?????? ???????  
???&??yyyy?????Ayyy¬yyya??L?? ???&?
?MathType??p????u?th??????O?ao?e ?icae?e iaceaa?oueny “??aiiaaaeia
noaoenoe/ia iaoai?ea iaiaeii??aeiiai ni?i-1/2 XY eaioethaeea”. Ooo
cai?iiiiiaaii /eneiaee iaoiae aeey iaiaeii??aeii? iaeiiaei??ii? XY
iiaeae? o iiia?a/iiio iie?, yea neeaaea?oueny c N ni?i?a aaee/eiith 1/2
o aoceao iaeiiaei??ii? ??aoee c aai?eueoii?aiii

wmetafile8? ??3/4???????????
???????????yyy????.????1?????? ??????? A
)???&??yyyy?????Ayyy»yyya(???? ???&?
?MathType??????u#yU?????aea j — cia/aiiy iiia?a/iiai iiey ia j-io
aoce?, a wmetafile8? ??Oe????????????
???????????yyy????.????1?????? ???????
 A???&??yyyy?????Ayyy¬yyy???L?? ???&?
?MathType??p????u?th??????

wmetafile8? ??›???????????
???????????yyy????.????1?????? ??????? A 
???&??yyyy?????Ayyy?yyy` ??o?? ???&? ?MathType???
???u?????????»????-?????HD???H,???H†???H6???u?
ya????? wmetafile8? ??J???????????
???????????yyy????.????1?????? ??????? 
????&??yyyy?????AyyyFyyyA??A?? ???&?
?MathType??A????uath??????1/4??????Times New Roman?????-??
???2–r???A?I? ???2–µ???B?A? ???2c3/4???B?A?
???2cu???A?I????u`y??????1/4??????Times New
Roman?????-??????? ???2a„???*?P?
???2aN???*?P????uath???????ici??o 2N2N, a eiao?oe??ioe eaiii?/iiai
ia?aoai?aiiy c ?? aeanieie aaeoi?aie. ?c niaeo?o aeanieo cia/aiue
io?eio?oueny u?euei?noue aeaiaioa?ieo caoaeaeaiue iiaeae?, a, ioaea, ?
oa?iiaeeiai?/i? ooieoe??. Iiia?a/io iaiaai?/ai?noue oa noaoe/io
iiia?a/io ni?eeiyoeea?noue io?eiothoue a iaeii??aeiiio aeiaaeeo,
aeeoa?aioe?thth/e a?eueio aia?a?th ca iiia?a/iei iieai. I?ioa, ine?eueee
ie ?ica’yco?ii caaea/o /enaeueii ? ia cia?ii yaii? caeaaeiino?
u?eueiino? ?iciiae?eo aeaiaioa?ieo caoaeaeaiue a?ae iiia?a/iiai iiey,
aeey ia/eneaiiy na?aaeiuei? iaiaai?/aiino? oa aeeiai?/ieo ei?aeyoe?eieo
ooieoe?e ne?ae ei?enooaaoenue yaieie ae?acaie na?aaei?o a?ae ni?iiaeo
iia?aoi??a. A ?acoeueoao?, aeey ia/eneaiiy na?aaei?o a?ae ni?iiaeo
iia?aoi??a iaiao?aeii ciaoe eiao?oe??ioe eaiii?/iiai ia?aoai?aiiy, ye? ?
aeanieie aaeoi?aie aei/ii? iao?eoe?.

Aeine?aeaeaiiy oa?aeoa?enoee nenoaie i?iaiaeeoueny oaeei /eiii:
?icaeyaea?ii ne?i/aiiee eaioethaeie aeiaaeeiith N, cia/aiiy iie?a ia
aoceao oa i?aeni?iiai? aca?iiae?? aeae?athoueny aaia?aoi?ii aeiaaeeiaeo
/enae ?c caaeaiei ?iciiae?eii ?iia??iino?. Aeae? caaea/a iiooeo aeanieo
cia/aiue aai?eueoii?aia, a?eueii? aia?a??, /aniaeo ei?aeyoe?eieo
ooieoe?e ?ica’yco?oueny /enaeueii aeey eiaeii? eiie?aoii? nenoaie. Iio?i
aaia?othoueny iia? nenoaie c oei naiei ?iciiae?eii ?iia??iino?. A e?ioe?
i?ioeano an? aaee/eie ona?aaeiththoueny ca iayaieie aeiaaeeiaeie
?aae?caoe?yie.

A ?iaio? oaeiae ?icaeyiooi /anoeii? aeiaaeee ni?i-1/2 ai?cio?iiii? XY
iiaeae? aac aca?iiae?? Aecyeioeinueeiai-Ii??y oa ?cio?iiii? iiaeae? c
aca?iiae??th Aecyeioeinueeiai-Ii??y. A ?cio?iiiiio aeiaaeeo ciaeaeaii
yaio caeaaei?noue u?eueiino? aeaiaioa?ieo caoaeaeaiue a?ae iino?eii?
neeaaeiai? iiia?a/iiai iiey wmetafile8? ??????????????
???????????yyy????.????1?????? ???????
?a???&??yyyy?????AyyyAyyy ??A?? ???&?
?MathType??P????u?th???????acoeueoaoe /eneiaiai i?aeoiaeo
ii??aiththoueny c a?aeiieie oi/ieie aiae?oe/ieie ?acoeueoaoaie aeey
iaeii??aeieo eaioethaee?a, i?e/iio aeyaeaii, ui i?aeoe/ii aaea nenoaia c
200 ni?iaie aeinoaoiuei aeia?a iieno? an? oa?iiaeeiai?/i? oa aeeiai?/i?
aeanoeaino?, i?ioa aeey ?ic?aooieo u?eueiino? aeaiaioa?ieo caoaeaeaiue
iio??aii a?aoe eaioethaeee ii?yaeeo 1000 ni?i?a, uia io?eiaoe
aeinoaoiuei aeaaeeo ?? oi?io. sse i?eeeaae ?iaioe iaoiaeo ia/eneaia
aeeiai?/ia ni?eeiyoeea?noue iaeiiaei??ii? ni?i-1/2 eaaioiai? iiaeae?
?c?i?a c aca?iiae??th Aecyeioeinueeiai-Ii??y, aeine?aeaeo?oueny ?? ci?ia
i?e aeeth/aii? aeiaaeeiaiai iiey.

I?e ?icaeyae? i?inoi? eaaioiai? iiaeae? ?c?i?a aac aca?iiae??
Aecyeioeinueeiai-Ii??y caaea/o ?ic?aooieo oa?aeoa?enoee iiaeae? iiaeia
caanoe aei ae?aaiiae?caoe?? ae?enii? o?eae?aaiiaeueii? iao?eoe? ?ici??ii
NN. Iiaeaeue ?c?i?a o aeiaaeeiaiio iiia?a/iiio iie?, yea iiaea i?eeiaoe
aeaa cia/aiiy ia aoce?

wmetafile8? ?????????????
???????????yyy????.????1?????? ???????
@`???&??yyyy?????AyyyAyyy ????? ???&?
?MathType??p????u?th??????*aoaa?oee ?icae?e iaceaa?oueny
“Aeine?aeaeaiiy iaaii?yaeeiaaii? iiaeae? ?c?i?a a iaaeeaeaii?
aeaioainoie”. Ia a?aei?io a?ae iiia?aaei?o ?icae?e?a a?i ia i?noeoue
oi/ieo ?ica’yce?a, a iia’ycaiee c iaoiaeii ooieoe?iiaeueiiai
?ioa??oaaiiy oa a?aenoiiaoaaiiyi ae?aa?ai iaaiiai oeio, ye? aeieeathoue
a oe?e oaoi?oe? i?e iaaeeaeaiiio ?ic?aooieo ooieoe?iiaeueieo ?ioa??ae?a.
A ?icae?e? ?icaeyaea?oueny aeaieiiiiiaioia iiaeaeue ?c?i?a, yeo iiaeia
iienaoe aai?eueoii?aiii:

wmetafile8? ??7???????????
???????????yyy????.????1?????? ???????
A@:???&??yyyy?????Ayyy?yyy?:??o?? ???&? ?MathType???
???u?????????»????-?????Ho ???HU
???Ho&???Ha’???u?th??????Ia?o? aeaa aeiaeaiee a?aeiia?aeathoue
iaaii?yaeeiaai?e ?iii?e i?aenenoai?. Ooo wmetafile8?
??????????????? ???????????yyy????.????1??????
???????   ???&??yyyy?????AyyyAyyya??a?? ???&?
?MathType??`????u?th??????wmetafile8? ??A???????????
???????????yyy????.????1?????? ???????
A`»???&??yyyy?????Ayyy»yyy «???? ???&? ?MathType???
???u?????????»????-?????<‚???<j???u?th??????aea wmetafile8? ??.??????????? ???????????yyy????.????1?????? ??????? ?a???&??yyyy?????AyyyAyyy ??A?? ???&? ?MathType??P????u?th??????Oa??iei ooieoe?iiaeii aeaii? nenoaie ? oa?iiaeeiai?/iee iioaioe?ae wmetafile8? ??‡??????????? ???????????yyy????.????1?????? ??????? ?????&??yyyy?????Ayyy¬yyy@??,?? ???&? ?MathType??`????u?th??????wmetafile8? ??-??????????? ???????????yyy????.????1?????? ??????? ?@(???&??yyyy?????Ayyy?yyy?(??*?? ???&? ?MathType??? ???u?????????"????-???????¬????H????H????@¬????? ? ???n ???n ???@ ???7???Aeine?aeaeaiiy oa?aeoa?enoee iiaeae? aeeiioaaeinue iaoiaeii ooieoe?iiaeueiiai ?ioa??oaaiiy, a iaaeeaeaia ia/eneaiiy ooieoe?iiaeueieo ?ioa??ae?a aoei cae?eniaii c aeei?enoaiiyi noioaaiiy ae?aa?ai ca?oiiaaieo ca iaa?iaiei ?aae?onii aca?iiae??. Aeae?eaiiy naiiocaiaeaeaiiai iiey wmetafile8? ??O??????????? ???????????yyy????.????1?????? ??????? ?@???&??yyyy?????AyyyAyyy???A?? ???&? ?MathType??P????u?th??????wmetafile8? ??a??????????? ???????????yyy????.????1?????? ??????? A@???&??yyyy?????AyyyAyyy?????? ???&? ?MathType???? ???u?????????"????-?????i???y???? ???h???u?th??????wmetafile8? ??„??????????? ???????????yyy????.????1?????? ??????? ?a2???&??yyyy?????Ayyy«yyy 2??«?? ???&? ?MathType??? ???u?????????"????-?????t?d????????????d???t ?x ????O ????O ????x ????f???????`?I????e????e???°I???`?e ????AE ????AE ???°e ????W ????o???t?©*????L*????L*????©*???t?A1????"2? ???"2????A1???uyTH?????wmetafile8? ??-??????????? ???????????yyy????.????1?????? ??????? ? ???&??yyyy?????Ayyy?yyy`????? ???&? ?MathType???? ???u?????????"????-?????„? ????|H????|H????t ????„ ?I???|'???|'???tI???u?th??????Noioaaiiy an?o ca?aeieo ca aeieii ae?oaiai ii?yaeeo ae?aa?ai i?eaiaeeoue aei iaaeeaeaiiy aeaioainoie. C oiiae noaoe?iia?iino? oa??iiai ooieoe?iiaeo io?eiothoue nenoaio 9-oe ??aiyiue aeey iaa?aeiieo aa??aoe?eieo ia?aiao??a. *enaeueii aeine?aeaeothoueny aeiaaeee iaeiieiiiiiaioii? iiaeae? ?c?i?a, iaiaai?oiiai a?ia?iiai nieaao oa ??aoeiaiai aaco. Aeey iaeiieiiiiiaioii? iiaeae? ?c?i?a io?eiaii oaiia?aoo?io caeaaei?noue ia?aiao?a ii?yaeeo a ??cieo iaaeeaeaiiyo. A?aeiii, ui a iaaeeaeaii? aeaioainoie aeieea? oaciaee ia?ao?ae I ?iaeo (Garanin D.A., Lutovinov V.S. Sol.St.Com., 1984, 50, 219-222). Ia a?aei?io a?ae iueiai iaaeeaeaiiy aaoniaeo oetheooaoe?e, yea iiaeia io?eiaoe, yeui na?aae noeoiiino? an?o iaoeaaeo ae?aa?ai a?aooaaoe eeoa aeai ia?o?, oi/a e aea? iaio oi/iee ?acoeueoao aeey Tc, ia i?noeoue iao?ce/ieo iaeanoae. Ine?eueee iaaeeaeaiiy aeaioainoie iao?ce/ia a ieie? e?eoe/ii? oaiia?aoo?e /eneia? aeine?aeaeaiiy aeey iaiaai?oieo a?ia?iiai nieaao oa ??aoeiaiai aaco i?iaiaeyoueny a iaaeeaeaii? aaoniaeo oetheooaoe?e, a ?acoeueoaoe ii??aiththoueny c iaaeeaeaiiyi iieaeoey?iiai iiey. I'yoee ?icae?e iaceaa?oueny "Iiaeaeue ?c?i?a c ??cieie oeiaie aca?iiae?e a iaoiae? aoaeoeaiiai iiey". Ooo ?icaeyaea?oueny iiaeaeue ?c?i?a c aeia?eueiith i?aeni?iiaith aca?iiae??th wmetafile8? ????????????? ???????????yyy????.????1?????? ??????? @ ???&??yyyy?????AyyyAyyy`????? ???&? ?MathType??p????u?th??????wmetafile8? ??e??????????? ???????????yyy????.????1?????? ??????? ` ???&??yyyy?????Ayyy¬yyya?? ?? ???&? ?MathType??wmetafile8? ??8??????????? ???????????yyy????.????1?????? ??????? aA???&??yyyy?????Ayyy3/4yyy?????? ???&? ?MathType??? ???u?????????"????-?????h????h????n?ae???hu??? hu???ssae???n?o???hc???hc???sso???u?th?????? ???i?G? ???2e???i?G? ???2®???J?p? ???2????S??? ???2‡ ???j?G????u@y?????? aeoiaeeoue, ui wmetafile8? ??i??????????? ???????????yyy????.????1?????? ??????? ?A???&??yyyy?????Ayyy?yyy???/?? ???&? ?MathType?? ? ???u?????????"????-?????Q??????EH????EH??????????Q ?? ???Ea???Ea????? ???u?th?????? Oea iaaeeaeaiiy aeicaiey? io?eiaoe ooieoe?th ?iciiae?eo caeaaeio eeoa a?ae na?aaeiueiai iaai?oiiai iiiaioo, ui ia a?aeaeaa? caeaaeiino? ?? a?ae oaiia?aoo?e i?e T>Tc. Iie?auaiiyi oeueiai iaaeeaeaiiy ? iaaeeaeaiiy
ei?aeyoe?eiiai aoaeoeaiiai iiey, yea iieyaa? a iaaeeaeaiiio cia?aaeaii?
ni?iiaeo iia?aoi??a ia ??cieo aoceao /a?ac ni?i ia aeae?eaiiio aoce?
wmetafile8? ???????????????
???????????yyy????.????1?????? ???????
@a???&??yyyy?????AyyyAyyy ????? ???&?
?MathType??p????u?th??????wmetafile8? ?????????????
???????????yyy????.????1?????? ???????
a????&??yyyy?????Ayyy3/4yyyA????? ???&? ?MathType???
???u?????????»????-?????h°???h~???u yU?????Iaoith
oeueiai ?icae?eo ? aea/aiiy aieeao aaee/eie ?aae?ona aca?iiae?? a iaaeao
?icaeyiooeo iaaeeaeaiue aoaeoeaiiai ? ei?aeyoe?eiiai aoaeoeaiiai iiey ia
iiaaae?ieo oa?iiaeeiai?/ieo ooieoe?e oa ooieoe?? ?iciiae?eo eieaeueieo
iie?a P(h). *a?ac ooieoe?th ?iciiae?eo P(h) iiaeia ae?aceoe iiia?a/iee
aeeiai?/iee no?oeoo?iee oaeoi? wmetafile8? ??•???????????
???????????yyy????.????1?????? ???????
``???&??yyyy?????AyyyAyyy ?? ?? ???&? ?MathType??°?
???u?????????»????-?????@?????|H????|H?????????@?c
???|L???|L????c???u?th??????

Iniiai? ?acoeueoaoe oa aeniiaee

1. A aeena?oaoe?ei?e ?iaio? aia?oa io?eiaii oi/i? ?acoeueoaoe aeey
oa?iiaeeiai?/ieo ooieoe?e iaeiiaei??ii? ni?i-1/2 ?cio?iiii? XY iiaeae? c
aca?iiae??th Aecyeioeinueeiai-Ii??y o aeiaaeeiaiio ei?aioeiaiio
iiia?a/iiio iie?. C’yniaaii, ui i?e ?ic?aooieao oa?iiaeeiai?/ieo
ooieoe?e a?aooaaiiy aca?iiae?? Aecyeioeinueeiai-Ii??y i?eaiaeeoue aei
ia?aii?ioaaiiy i?aeaoceiai? aca?iiae??.

2. Ia i?eeeaae? oaei? iiaeae? aeine?aeaeaii iaae? canoiniaiino?
iaaeeaeaiiy eiiooaoe?eieo ni?aa?aeiioaiue Aica oa iaaeeaeaiiy oeio
Oyae?eiaa. Aeyaeaii, ui aeey aeiaaeeiaiai ei?aioeiaiai iiia?a/iiai iiey
oe? iaaeeaeaiiy i?eaiaeyoue aei ?ica?aeiino? noaoenoe/ii? noie /a?ac
aeieeiaiiy aica-caoaeaeaiue c a?ae’?iiith aia?a??th.

3. Ia i?eeeaae? oaei? iiaeae? aeyaeaii, ui ca oiiae, eiee
oa?iiaeeiai?/ia ona?aaeiaiiy i?iaaaeaii oi/ii, iaeiiaoceiaa iaaeeaeaiiy
eiaa?aioiiai iioaioe?aeo caaeia?eueii iieno? nenoaie, ye c iaia?a?aiei,
oae ? c aeene?aoiei ?iciiae?eii aeiaaeeiaeo ia?aiao??a aai?eueoii?aia.

4. Cai?iiiiiaaii iaaeeaeaiee i?aeo?ae aeey iieno iaeiiaei??ii? ni?i-1/2
XXZ iiaeae? Aaecaiaa??a c aca?iiae??th Aecyeioeinueeiai-Ii??y o
aeiaaeeiaiio ei?aioeiaiio iiia?a/iiio iie?, yeee ??oioo?oueny ia
oa?i?-cia?aaeaii? aai?eueoii?aia c ianooiiei aeei?enoaiiy iaaeeaeaiiy
Oa?o??-Oiea.

5. *eneiaee iaoiae aeey aeine?aeaeaiiy ne?i/aiieo ni?i-1/2 XY
eaioethaee?a o iiia?a/iiio iie? canoiniaaii aei aeine?aeaeaiiy iiaeae?
?c?i?a o aeiaaeeiaiio iiia?a/iiio iie? c aca?iiae??th
Aecyeioeinueeiai-Ii??y. Iieacaii, ye aaceaae ?oeio? oa?aeoa?iee
/anoioiee i?io?eue iiia?a/ii? aeeiai?/ii? ni?eeiyoeeaino?, coiiaeaii?
aca?iiae??th Aecyeioeinueeiai-Ii??y.

6. Aeine?aeaeaii oa?iiaeeiai?/i? oa ei?aeyoe?ei? ooieoe?? iaeiiaei??ii?
iiaeae? ?c?i?a o aeiaaeeiaiio iiia?a/iiio iie?. Aeey iiaeae? o
aeiaaeeiaiio iiia?a/iiio iie?, yea iiaea i?eeiaoe aeaa cia/aiiy, iaeia c
yeeo 0, anoaiiaeaii oiiae, ca yeeo a nenoai? aeieeathoue aeaiaioa?i?
caoaeaeaiiy c aeecueeeie aei ioey aia?a?yie, ui ci?ith?
iecueeioaiia?aoo?iee o?ae oaiei?iiino?. Iieacaii, ui i?e iecueeeo
eiioeaio?aoe?yo aoce?a c ioeueiaei iiia?a/iei iieai zz-ei?aeyoe?eia
aeiaaeeia o aeiaaeeia?e nenoai? c?inoa? a ii??aiyii? c iaeii??aeiith.

7. Aeey aeine?aeaeaiiy oa?iiaeeiai?ee iaaii?yaeeiaaii? aeaieiiiiiaioii?
iiaeae? ?c?i?a o ?aieao ?icaeiaiue ca iaa?iaiei ?aae?onii aca?iiae??
noi?ioeueiaaii ?yae iaaeeaeaiue ca aeaeaeiae??th c aaceniei a?aooaaiiyi
ei?ioeinyaeieo aca?iiae?e. Ia/eneaii oa?iiaeeiai?/i? ooieoe?? e
iiaoaeiaaii oacia? ae?aa?aie o aeiaaeeao iaiaai?oiiai a?ia?iiai nieaao ?
??aoeiaiai aaco.

8. Ocaaaeueiaii iaoiae aoaeoeaiiai iiey ia aeiaaeie iiaeae? ?c?i?a c
aeia?eueiith aca?iiae??th. Ia i?eeeaae? aeniiiaioe?eii niaaeii?
i?aeaoceiai? aca?iiae?? aeine?aeaeaii caeaaei?noue oi?ie e?i?? ooieoe??
?iciiae?eo eieaeueieo iie?a a?ae ?aae?ona aca?iiae??. Ia/eneaii
iaiaai?/ai?noue ? noaoe/io ni?eeiyoeea?noue aeey aeaii? iiaeae? c
??cieie aca?iiae?yie.

9. Iaaeeaeaiiy ei?aeyoe?eiiai aoaeoeaiiai iiey aeey iiaeae? ?c?i?a
ocaaaeueiaii ia aeiaaeie aca?iiae?? aeia?eueiiai ?aae?ona. Aeaia
iaaeeaeaiiy, ia a?aei?io a?ae iaaeeaeaiiy aoaeoeaiiai iiey, aeicaiey?
aeine?aeeoe caeaaei?noue ooieoe?? ?iciiae?eo eieaeueieo iie?a i?e
oaiia?aoo?ao aeueo ca e?eoe/io.

?acoeueoaoe aeena?oaoe?? iioae?eiaaii a oaeeo ?iaioao:

1. Derzhko O., Krokhmalskii T., Verkholyak T. Thermodynamical properties
of random spin-1/2 XY chain with Dzyaloshinskii-Moriya interaction. //
JMMM, 1996, vol.157/158, p.421-423.

2. Derzhko O., Verkholyak T. One-dimensional spin-1/2 XY model as a test
for methods in the spin system theory. // phys.stat.sol. (b), 1997,
vol.200, 1, p.255-263.

3. Derzhko O., Krokhmalskii T., Verkholyak T. Thermodynamical and
dynamical properties of quenched quantum spin chains. // Material
Science & Engineering A, 1997, vol.226-228, p.1049-1052.

4. Derzhko O., Verkholyak T. One exactly solvable magnetic chain with
quenched randomness. // Material Science & Engineering A, 1997,
vol.226-228, p.745-748.

5. Derzhko O.V., Verkholyak T.M. One exactly solvable random spin-1/2 XY
chain. // OIO, 1997, o.23, 9, p.977-982.

6. Derzhko O., Krokhmalskii T., Verkholyak T. Thermodynamics and spin
correlations for Ising chain in random transverse field. //
Philosophical Magazine B, 1997, vol.76, 5, p.855-858.

7. Sorokov S.I., Levitskii R.R., Verkholyak T.M. Effective field method
for Ising model with arbitrary ferromagnetic interaction. //
phys.stat.sol. (b), 1999, vol.211, 2, p.759-769.

8. Derzhko O., Krokhmalskii T., Verkholyak T. Thermodynamical properties
of random spin-1/2 XY chain with Dzyaloshinskii-Moriya interaction.
//Miramare — Trieste, 1995, 7p. (Internal Report / International Centre
for Theoretical Physics; IC/95/181).

9. Derzhko O., VerkholyakT. 1D spin-1/2 XY model as a testing ground for
spin systems theory methods. //Miramare — Trieste, 1995, 10p. (Internal
Report / International Centre for Theoretical Physics; IC/95/182).

10. Derzhko O.V., Verkholyak T.M. Spin-1/2 isotropic XY chain with
Dzyaloshinskii-Moriya interaction in random lorentzian transverse field.
— Lviv, 1996, 33p. (Preprint / Institute for Condensed Matter Physics;
ICMP-96-25E).

11. Sorokov S.I., Levitskii R.R., Verkholyak T.M. Investigation of the
annealed disordered Ising systems within two-tail approximation. — Lviv,
1996, 19p. (Preprint / Institute for Condensed Matter Physics;
ICMP-96-26E).

12. Sorokov S.I., Levitskii R.R., Verkholyak T.M. Local field method for
Ising model with arbitrary interaction. — Lviv, 1997, 15p. (Preprint /
Institute for Condensed Matter Physics; ICMP-97-20E).

13. Ni?ieia N.?., Eaaeoeueeee ?.?., Aa?oieye O.I. Aeine?aeaeaiiy iiaeae?
?c?i?a iaoiaeii aoaeoeaiiai iiey. — Euea?a, 1999, 25n. (I?ai?eio /
?inoeooo o?ceee eiiaeainiaaieo nenoai; ICMP-99-04U).

14. Verkholyak T. Damping of spin correlations in random quantum Ising
chains. — In.: International workshop on statistical physics and
condensed matter theory (Sept.11-14, 1995, Lviv, Ukraine). Programme and
abstracts, p.95.

15. Derzhko O., Verkholyak T. One exactly solvable magnetic chain with
quenched randomness. — In: Ninth International Conference on rapidly
Quenched and Metastable Materials. Book of abstracts. RQ9, Bratislava,
August 25-30, 1996, p.346.

16. Sorokov S.I., Levitskii R.R., Verkholyak T.M. Local field method for
Ising model with arbitrary interaction. // International Seminar & Phase
Transition and Critical Phenomena, Poznan, Poland, December 4-6, 1997,
p.19.

17. Sorokov S.I., Verkholyak T.M. Correlated effective field
approximation for Ising model with arbitrary interaction. // In:
INTAS-Ukraine Workshop on Condensed Matter Physics. Lviv, May 21-24,
1998, p.114.

Aa?oieye O.I. Aieea aaceaaeo oa ??cieo oei?a aca?iiae?? ia
oa?iiaeeiai?/i? oa aeeiai?/i? aeanoeaino? iiaeaeueieo ni?iiaeo nenoai. —
?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.04.02 – oai?aoe/ia
o?ceea. ?inoeooo o?ceee eiiaeainiaaieo nenoai Iaoe?iiaeueii? aeaaeai??
iaoe Oe?a?ie, Euea?a, 1999.

Aeena?oaoe?th i?enay/aii oai?aoe/iiio aeine?aeaeaiith aieeao aaceaaeo oa
??cieo oei?a aca?iiae?? ia oa?iiaeeiai?/i? oa aeeiai?/i? aeanoeaino?
iiaeaeueieo ni?iiaeo nenoai. Aeey aeiaaeeiaeo ni?i-1/2 XY eaioethaee?a
cai?iiiiiaaii /eneiaee iaoiae aeine?aeaeaiiy oa?iiaeeiai?/ieo oa
ei?aeyoe?eieo ooieoe?e. O aeiaaeeo ?cio?iiiiai eaioethaeea caaea/a
caaaeaia aei caaea/? Eeieaea oa ?ica’ycaia oi/ii. Aeey aeine?aeaeaiiy
aeaieiiiiiaioii? iaaii?yaeeiaaii? iiaeae? ?c?i?a canoiniao?oueny
ae?aa?aiia oaoi?ea oa iaai?ththoueny iaaeie?ee ??cieo iaaeeaeaiue.
Aeine?aeaeai? aeeiai?/i? aeanoeaino? iaeii??aeii? iiaeae? ?c?i?a a
iaaeeaeaii? aoaeoeaiiai iiey. Iieacaii ye o oae?e iiaeae? aeieea?
ne?i/aiia oe?eia e?i?e iaai?oiiai ?aciiaino aiane?aeie aeaeaeinyaeiino?
aca?iiae??.

Eeth/ia? neiaa: ni?iia? iiaeae?, iaaii?yaeeiaai? nenoaie,
oa?iiaeeiai?ea, ei?aeyoe?ei? ooieoe??.

Aa?oieye O.I. Aeeyiea aanii?yaeea e acaeiiaeaenoaee ?aciuo oeiia ia
oa?iiaeeiaie/aneea e aeeiaie/aneea naienoaa iiaeaeueiuo nieiiauo nenoai.
— ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.04.02 – oai?aoe/aneay
oeceea. Einoeooo oeceee eiiaeaine?iaaiiuo nenoai Iaoeeiiaeueiie
aeaaeaiee iaoe Oe?aeiu, Eueaia, 1999.

Aeenna?oaoeey iinayuaia oai?aoe/aneiio enneaaeiaaieth aeeyiey
aanii?yaeea e ?aciuo oeiia acaeiiaeaenoaee ia oa?iiaeeiaie/aneea e
aeeiaie/aneea naienoaa iiaeaeueiuo nieiiauo nenoai. Aeey neo/aeiuo
niei-1/2 XY oeaii/ae i?aaeeiaeai iaoiae enneaaeiaaiey oa?iiaeeiaie/aneeo
e ei??aeyoeeiiiuo ooieoeee. A neo/aa ecio?iiiie oeaii/ee caaea/a
naiaeeony e caaea/a Eeieaea e ?aoaaony oi/ii. Aeey enneaaeiaaiey
aeaooeiiiiiaioiie iaoii?yaei/aiiie iiaeaee Eceiaa i?eiaiyaony
aeeaa?aiiiay oaoieea e ianoaeaeathony iaaeinoaoee ?aciuo i?eaeeaeaiee.
Enneaaeiaaiu aeeiaie/aneea naienoaa iaeii?iaeiie iiaeaee Eceiaa a
i?eaeeaeaiee yooaeoeaiiai iiey. Iieacaii eae a aeaiiie iiaeaee
iiyaeyaony eiia/iay oe?eia eeiee iaaieoiiai ?aciiaina aneaaenoaee
aeaeueiiaeaenoaey acaeiiaeaenoaey.

Eeth/aaua neiaa: nieiiaua iiaeaee, iaoii?yaei/aiiua nenoaiu,
oa?iiaeeiaieea, ei??aeyoeeiiiua ooieoeee.

Verkholyak T.M. Influence of disorder and different types of
interactions on the thermodynamic and dynamic properties of the model
spin systems. — Manuscript.

Thesis on search of the scientific degree of candidate of physical and
mathematical sciences, speciality 01.04.02 – theoretical physics.
Institute for Condensed Matter Physics of the Ukrainian National Academy
of Sciences, Lviv, 1999.

Theoretical study of how disorder and different types of interactions
influence the thermodynamic and dynamic properties of spin systems is
the subject of the presented thesis. The models with equilibrium and
nonequilibrium disorder are considered.

For the one-dimensional spin-1/2 isotropic XY model with
Dzyaloshynskii-Moriya interaction in random Lorentzian transverse field,
the density of elementary excitations and the thermodynamic functions
are found exactly using the Jordan-Wigner transformation and mapping the
considered model to the model of free fermion on the one dimensional
lattice. The average density of elementary excitations, transverse
magnetization, static susceptibility are investigated numerically at
different values of Dzyaloshinskii-Moriya interaction D. It is found out
how this interaction renormalizes the isotropic interaction of the
model. It is also shown that the random field causes disappearance of
quantum phase transition at T=0. In virtue of the obtained exact
results, some well known approximations are tested. It is found out that
the Bose commutation rules approximation and the Tyablikov-like
approximation cannot be applied to the model in random Lorentzian field
because there arise the excitations with negative value of energy and
the partition function of the model diverges. The results of the
coherent potential approximation for the density of elementary
excitations show a good agreement with the exact analytical and
numerical results for the model with both continuous and discrete
distribution functions of random parameters of the Hamiltonian. With the
help of the Jordan-Wigner transformation, the approximate method for the
spin-1/2 XXZ Heisenberg chain with Dzyaloshynskii-Moriya interaction in
random Lorentzian transverse field is proposed. It is based on
Hartree-Fock-like approximation for the fermionized spin Hamiltonian.

The exact numerical approach based on the fermionization procedure is
applied to the finite spin-1/2 XY chains with arbitrary distribution
functions of Hamiltonian parameters and with the antisymmetric
interaction between x and y components of spin. The Hamiltonian is the
quadratic form in fermionic representation, and the calculation of the
thermodynamic and dynamic functions is reduced to solving the eigenvalue
and eigenvector problem of a certain 2N2N matrix. It allows one to
consider sufficiently long chains consisting of 1000 spins or even more.
The transverse dynamic susceptibility of the quantum Ising chain with
Dzyaloshynskii-Moriya interaction in random Gaussian transverse field is
calculated. It is demonstrated how the random field destroys the
frequency shape of transverse dynamic susceptibility of such a model.
The thermodynamic and correlation functions of the Ising chain in random
transverse field are studied in details. If the random field can be
equal to zero, it is determined the conditions, when the elementary
excitations of low energy arise. These excitations cause the change of
the specific heat at low temperatures. It is also found that the
transverse correlation function for such a random model can increase in
comparison with that of the uniform model.

The equilibrium disorder effect on the spin model properties is studied
by using the Ising model with the binary disorder. The method of series
expansion in inverse interaction radius is generalized for this purpose.
The expressions for the thermodynamic potential and correlation
functions are obtained within the two-tail and Gaussian fluctuation
approximations. Because of two-tail approximation gives non-physical
results in the critical temperature vicinity, all calculations are
performed within the Gaussian fluctuation approximation. Phase diagrams
(binodal and spinodal curves) for non-magnetic binary alloy, and the
isoterms and coexistence curves for non-magnetic lattice gas are
obtained.

To study the influence of the interaction radius on the physical
characteristics of the Ising model, the effective field method is
extended for the models with an arbitrary interaction. Using the
integral representation of Callen identity the thermodynamic functions
are expressed through the local field distribution function P(h) and
found within the effective and correlated effective field approximation.
P(h) can also describe some dynamic characteristics because the
transverse dynamic structure factor is proportional to it. We studied
the influence of the interaction radius on the thermodynamic function
and the structure of the local field distribution function for the model
with exponentially decaying interaction. We investigated how the shape
of the local field distribution function changes from the Gaussian-like
one for the large interaction radius to the set of peaks with finite
linewidth for smaller magnitudes of the radius. It is found that taking
into account spin correlations within the correlated effective field
approximation does not change the shape of P(h) but only increases the
fluctuations of local field.

Key words: spin models, disordered systems, thermodynamics, correlation
functions.

I?aeienaii aei ae?oeo 18.08.99. Oi?iao 60×84/16.

Ae?oe ionaoiee. Oi. ae?oe. a?e. 1,0. Oe?aae 100. Cai. 5052.

Ae?oe IOO ? 58 290008, Euea?a, aoe. ?a. Oaaei?iaa, 9.

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