Condensed Matter Physics, 2012, vol. 15, No. 4, p. 43005:18
DOI:10.5488/CMP.15.43005
arXiv:1212.6137
Title:
Goldstone mode singularities in O(n) models
Author(s):

J. Kaupužs
(Institute of Mathematics and Computer Science, University of Latvia, 29 Raiņa Boulevard, LV1459 Riga, Latvia; Institute of Mathematical Sciences and Information Technologies, University of Liepaja, 14 Liela St., Liepaja LV3401, Latvia)
,


R.V.N. Melnik
(Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5)
,


J. Rimšāns
(Institute of Mathematics and Computer Science, University of Latvia, 29 Raiņa Boulevard, LV1459 Riga, Latvia; Institute of Mathematical Sciences and Information Technologies, University of Liepaja, 14 Liela St., Liepaja LV3401, Latvia)

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 threedimensional 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 nontrivial (3/2<λ_{⊥}<2 and 0<λ_{}<1 in three dimensions) and the ratio b M^{2}/a^{2} (where M is a spontaneous magnetization) is universal. The trivial standardtheoretical 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 2λ_{⊥} decreases for large n and tends to zero at n → ∞. We have also verified and confirmed the expected universality of b M^{2}/a^{2} for the O(4) model, where simulations at two different temperatures (couplings) have been performed.
Key words:
Monte Carlo simulation, ncomponent vector models, correlation functions,
PACS:
05.10.Ln, 75.10.Hk, 05.50.+q
