Title: Goldstone mode singularities in O(n) models
Author(s):

	J. Kaupužs (Institute of Mathematics and Computer Science, University of Latvia, 29 Raiņa Boulevard, LV-1459 Riga, Latvia; Institute of Mathematical Sciences and Information Technologies, University of Liepaja, 14 Liela St., Liepaja LV-3401, 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, LV-1459 Riga, Latvia; Institute of Mathematical Sciences and Information Technologies, University of Liepaja, 14 Liela St., Liepaja LV-3401, 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 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.

Key words: Monte Carlo simulation, n-component vector models, correlation functions,
PACS: 05.10.Ln, 75.10.Hk, 05.50.+q

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