Goldstone mode singularities in O(n) models

• Дата: 2012
• Автори: Kaupužs, J., Melnik, R.V.N., Rimšāns, J.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут фізики конденсованих систем НАН України 2012
• Назва видання: Condensed Matter Physics
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/120303
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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.

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.