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

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.