Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging
The critical behaviour of systems belonging to the three-dimensional Ising universality class is studied theoretically using the collective variables (CV) method. The partition function of a one-component spin system is calculated by the integration over the layers of the CV phase space in the appro...
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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2012
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/120304 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging / I.V. Pylyuk, M.V. Ulyak // Condensed Matter Physics. — 2012. — Т. 15, № 4. — С. 43006:1-10. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1203042017-06-12T03:04:49Z Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging Pylyuk, I.V. Ulyak, M.V. The critical behaviour of systems belonging to the three-dimensional Ising universality class is studied theoretically using the collective variables (CV) method. The partition function of a one-component spin system is calculated by the integration over the layers of the CV phase space in the approximation of the non-Gaussian sextic distribution of order-parameter fluctuations (the ρ⁶ model). A specific feature of the proposed calculation consists in making allowance for the dependence of the Fourier transform of the interaction potential on the wave vector. The inclusion of the correction for the potential averaging leads to a nonzero critical exponent of the correlation function η and the renormalization of the values of other critical exponents. The contributions from this correction to the recurrence relations for the ρ⁶ model, fixed-point coordinates and elements of the renormalization-group linear transformation matrix are singled out. The expression for a small critical exponent η is obtained in a higher non-Gaussian approximation. З використанням методу колективних змiнних (КЗ) вивчається критична поведiнка систем, якi належать до класу унiверсальностi тривимiрної моделi Iзинга. Статистична сума однокомпонентної спiнової системи обчислюється шляхом iнтегрування за шарами фазового простору КЗ в наближеннi негаусового шестирного розподiлу флуктуацiй параметра порядку (модель ρ⁶). Особливiстю запропонованого розрахунку є прийняття до уваги залежностi фур’є-образу потенцiалу взаємодiї вiд хвильового вектора. Врахування поправки на усереднення потенцiалу приводить до вiдмiнного вiд нуля критичного показника кореляцiйної функцiї η i перенормування значень iнших критичних показникiв. Видiлено внески вiд цiєї поправки в рекурентнi спiввiдношення для моделi ρ⁶, координати фiксованої точки та елементи матрицi лiнiйного перетворення ренормалiзацiйної групи. Вираз для малого критичного показника η отримано у вищому негаусовому наближеннi. 2012 Article Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging / I.V. Pylyuk, M.V. Ulyak // Condensed Matter Physics. — 2012. — Т. 15, № 4. — С. 43006:1-10. — Бібліогр.: 20 назв. — англ. PACS: 05.50.+q, 64.60.F-, 75.10.Hk DOI:10.5488/CMP.15.43006 arXiv:1212.6139 http://dspace.nbuv.gov.ua/handle/123456789/120304 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The critical behaviour of systems belonging to the three-dimensional Ising universality class is studied theoretically using the collective variables (CV) method. The partition function of a one-component spin system is calculated by the integration over the layers of the CV phase space in the approximation of the non-Gaussian sextic distribution of order-parameter fluctuations (the ρ⁶ model). A specific feature of the proposed calculation consists in making allowance for the dependence of the Fourier transform of the interaction potential on the wave vector. The inclusion of the correction for the potential averaging leads to a nonzero critical exponent of the correlation function η and the renormalization of the values of other critical exponents. The contributions from this correction to the recurrence relations for the ρ⁶ model, fixed-point coordinates and elements of the renormalization-group linear transformation matrix are singled out. The expression for a small critical exponent η is obtained in a higher non-Gaussian approximation. |
| format |
Article |
| author |
Pylyuk, I.V. Ulyak, M.V. |
| spellingShingle |
Pylyuk, I.V. Ulyak, M.V. Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging Condensed Matter Physics |
| author_facet |
Pylyuk, I.V. Ulyak, M.V. |
| author_sort |
Pylyuk, I.V. |
| title |
Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging |
| title_short |
Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging |
| title_full |
Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging |
| title_fullStr |
Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging |
| title_full_unstemmed |
Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging |
| title_sort |
critical behaviour of a 3d ising-like system in the ρ⁶ model approximation: role of the correction for the potential averaging |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120304 |
| citation_txt |
Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging / I.V. Pylyuk, M.V. Ulyak // Condensed Matter Physics. — 2012. — Т. 15, № 4. — С. 43006:1-10. — Бібліогр.: 20 назв. — англ. |
| series |
Condensed Matter Physics |
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AT pylyukiv criticalbehaviourofa3disinglikesysteminther6modelapproximationroleofthecorrectionforthepotentialaveraging AT ulyakmv criticalbehaviourofa3disinglikesysteminther6modelapproximationroleofthecorrectionforthepotentialaveraging |
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2023-10-18T20:36:40Z |
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2023-10-18T20:36:40Z |
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1796150646555017216 |