Goldstone mode singularities in O(n) models
Monte Carlo (MC) analysis of the Goldstone mode singularities for the transverse and the longitudinal correlation functions, behaving as G⊥ (k) ≅ a k-λ⊥ and G|| (k) ≅ b k-λ|| in the ordered phase at k → 0, is performed in the three-dimensional O(n) models with n=2,4,10. Our aim is to test some chall...
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Інститут фізики конденсованих систем НАН України
2012
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| Schriftenreihe: | Condensed Matter Physics |
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| Zitieren: | Goldstone mode singularities in O(n) models / J. Kaupužs, R.V.N. Melnik, J. Rimšāns // Condensed Matter Physics. — 2012. — Т. 15, № 4. — С. 43005:1-8. — Бібліогр.: 18 назв. — англ. |
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irk-123456789-1203032017-06-12T03:04:23Z Goldstone mode singularities in O(n) models Kaupužs, J. Melnik, R.V.N. Rimšāns, J. Monte Carlo (MC) analysis of the Goldstone mode singularities for the transverse and the longitudinal correlation functions, behaving as G⊥ (k) ≅ a k-λ⊥ and G|| (k) ≅ b k-λ|| in the ordered phase at k → 0, is performed in the three-dimensional O(n) models with n=2,4,10. Our aim is to test some challenging theoretical predictions, according to which the exponents λ⊥ and λ|| are non-trivial (3/2<λ⊥<2 and 0<λ||<1 in three dimensions) and the ratio b M²/a² (where M is a spontaneous magnetization) is universal. The trivial standard-theoretical values are λ⊥=2 and λ||=1. Our earlier MC analysis gives λ⊥=1.955 ± 0.020 and λ|| about 0.9 for the O(4) model. A recent MC estimation of λ||, assuming corrections to scaling of the standard theory, yields λ|| = 0.69 ± 0.10 for the O(2) model. Currently, we have performed a similar MC estimation for the O(10) model, yielding λ⊥ = 1.9723(90). We have observed that the plot of the effective transverse exponent for the O(4) model is systematically shifted down with respect to the same plot for the O(10) model by Δ λ⊥ = 0.0121(52). It is consistent with the idea that 2-λ⊥ decreases for large n and tends to zero at n → ∞. We have also verified and confirmed the expected universality of b M²/a² for the O(4) model, where simulations at two different temperatures (couplings) have been performed. У тривимiрних O(n) моделях з n = 2,4,10 здiйснено аналiз методом Монте Карло (МК) сингулярностей голдстоунiвських мод для поперечної i поздовжньої кореляцiйних функцiй, якi поводять себе як G⊥(k) ' ak−λ⊥ i G∥(k) ' bk−λ∥ у впорядкованiй фазi при k → 0. Нашою метою є перевiрити цiкавi теоретичнi передбаченя, згiдно яких iндекси λ⊥ i λ∥ є нетривiальними (3/2 < λ⊥ < 2 i 0 < λ∥ < 1 у трьох вимiрах) i коефiцiєнт bM²/a² (де M є спонтанною намагнiченiстю) є унiверсальний. Тривiальнi стандартнi теоретичнi значення є λ⊥ = 2 i λ∥ = 1. Наш попереднiй МК аналiз дає λ⊥ = 1.955±0.020 i λ∥ приблизно рiвне 0.9 для O(4) моделi. Недавня МК оцiнка λ∥, яка допускає поправки для скейлiнга стандартної моделi, дає λ∥ = 0.69±0.10 для O(2) моделi. Тепер ми здiйснили подiбну МК оцiнку для O(10) моделi, яка дає λ⊥ = 1.9723(90). Ми побачили, що графiк ефективного поперечного iндекса для O(4) моделi є систематично зсунутий вниз по вiдношенню до графiка для O(10) моделi на ∆λ⊥ = 0.0121(52). Це узгоджується з думкою, що 2−λ⊥ зменшується для великих n i прямує до нуля при n → ∞. Ми також перевiрили i пiдтвердили очiкувану унiверсальнiсть bM²/a² для O(4) моделi, для якої було здiйснено симуляцiї при двох рiзних температурах. 2012 Article Goldstone mode singularities in O(n) models / J. Kaupužs, R.V.N. Melnik, J. Rimšāns // Condensed Matter Physics. — 2012. — Т. 15, № 4. — С. 43005:1-8. — Бібліогр.: 18 назв. — англ. PACS: 05.10.Ln, 75.10.Hk, 05.50.+q DOI:10.5488/CMP.15.43005 arXiv:1212.6137 http://dspace.nbuv.gov.ua/handle/123456789/120303 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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English |
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Monte Carlo (MC) analysis of the Goldstone mode singularities for the transverse and the longitudinal correlation functions, behaving as G⊥ (k) ≅ a k-λ⊥ and G|| (k) ≅ b k-λ|| in the ordered phase at k → 0, is performed in the three-dimensional O(n) models with n=2,4,10. Our aim is to test some challenging theoretical predictions, according to which the exponents λ⊥ and λ|| are non-trivial (3/2<λ⊥<2 and 0<λ||<1 in three dimensions) and the ratio b M²/a² (where M is a spontaneous magnetization) is universal. The trivial standard-theoretical values are λ⊥=2 and λ||=1. Our earlier MC analysis gives λ⊥=1.955 ± 0.020 and λ|| about 0.9 for the O(4) model. A recent MC estimation of λ||, assuming corrections to scaling of the standard theory, yields λ|| = 0.69 ± 0.10 for the O(2) model. Currently, we have performed a similar MC estimation for the O(10) model, yielding λ⊥ = 1.9723(90). We have observed that the plot of the effective transverse exponent for the O(4) model is systematically shifted down with respect to the same plot for the O(10) model by Δ λ⊥ = 0.0121(52). It is consistent with the idea that 2-λ⊥ decreases for large n and tends to zero at n → ∞. We have also verified and confirmed the expected universality of b M²/a² for the O(4) model, where simulations at two different temperatures (couplings) have been performed. |
| format |
Article |
| author |
Kaupužs, J. Melnik, R.V.N. Rimšāns, J. |
| spellingShingle |
Kaupužs, J. Melnik, R.V.N. Rimšāns, J. Goldstone mode singularities in O(n) models Condensed Matter Physics |
| author_facet |
Kaupužs, J. Melnik, R.V.N. Rimšāns, J. |
| author_sort |
Kaupužs, J. |
| title |
Goldstone mode singularities in O(n) models |
| title_short |
Goldstone mode singularities in O(n) models |
| title_full |
Goldstone mode singularities in O(n) models |
| title_fullStr |
Goldstone mode singularities in O(n) models |
| title_full_unstemmed |
Goldstone mode singularities in O(n) models |
| title_sort |
goldstone mode singularities in o(n) models |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120303 |
| citation_txt |
Goldstone mode singularities in O(n) models / J. Kaupužs, R.V.N. Melnik, J. Rimšāns // Condensed Matter Physics. — 2012. — Т. 15, № 4. — С. 43005:1-8. — Бібліогр.: 18 назв. — англ. |
| series |
Condensed Matter Physics |
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