Eur. Phys. J. B 55, 363-370 (2007)
https://doi.org/10.1140/epjb/e2007-00064-0

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

¹ Institute of Mathematics and Computer Science, University of Latvia, 29 Rainja Boulevard, 1459 Riga, Latvia
² Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada

Corresponding author: ^a kaupuzs@latnet.lv

Received: 8 August 2006
Revised: 17 January 2006
Published online: 7 March 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 β=0.5, and β=0.55 in the ordered phase. We examine the prediction of the standard theory that the longitudinal susceptibility χ_∥ has a Goldstone mode singularity such that χ_∥ ∝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 χ_∥ ∝h^ρ-1, where 1/2<ρ<1 is a universal exponent related to the ∼h^ρ variation of the magnetization.