Equation of state and Goldstone-mode effects of the three-dimensional O(2) model

TL;DR

This study numerically investigates the three-dimensional O(2) model, focusing on Goldstone-mode effects, critical amplitudes, and scaling behavior of magnetization under varying magnetic fields, providing detailed insights into its magnetic equation of state.

Contribution

It offers a comprehensive numerical analysis of the 3D O(2) model, including Goldstone-mode effects, critical amplitudes, and scaling functions, with nonperturbative determination of coefficients.

Findings

Goldstone modes influence magnetization dependence on H.

Critical amplitudes are determined with negative corrections-to-scaling.

The O(2) scaling function has a smaller slope than the O(4) model.

Abstract

We investigate numerically the three-dimensional O(2) model on 8^3-160^3 lattices as a function of the magnetic field H. In the low-temperature phase we verify the H-dependence of the magnetization M induced by Goldstone modes and determine M in the thermodynamic limit both by extrapolation and by chiral perturbation theory. This enables us to calculate the corresponding critical amplitude. At T_c the critical scaling behaviour of the magnetization as a function of H is used to determine another critical amplitude. In both cases we find negative corrections-to-scaling. Our low-temperature results are well described by the perturbative form of the model's magnetic equation of state, with coefficients determined nonperturbatively from our data. The O(2) scaling function for the magnetization is found to have a smaller slope than the one for the O(4) model.