Monte Carlo test of the Goldstone mode singularity in 3D XY model

Kaupuzs J., Melnik, R.V.N., and Rimshans, J.

European Physical Journal B, 55 (4), 363-370, 2007

Abstract:

Monte Carlo simulations of magnetization and susceptibility in the 3D XY model are performed for system sizes up to L = 384 (significantly exceeding the largest size L = 160 considered in work published previously), and fields h >= 0.0003125 at two different coupling constants beta = 0.5, and beta = 0.55 in the ordered phase. We examine the prediction of the standard theory that the longitudinal susceptibility. chi(parallel to) has a Goldstone mode singularity such that chi(parallel to) proportional to h(-1/2) holds when h -> 0. Most of our results, however, support another theoretical prediction that the singularity is of a more general form chi(parallel to) proportional to h(rho-1), where 1/2 < rho < 1 is a universal exponent related to the similar to h(rho) variation of the magnetization.