A numerical study of Goldstone-mode effects and scaling functions of the three-dimensional O(2) model

TL;DR

This paper numerically analyzes the three-dimensional O(2) model, focusing on Goldstone-mode effects, scaling functions, and finite-size scaling, providing detailed insights into its critical behavior and comparison with related models.

Contribution

It presents a comprehensive numerical study of the 3D O(2) model, including Goldstone-mode effects, critical amplitudes, and scaling functions, with implications for QCD lattice data.

Findings

Goldstone modes influence magnetization dependence on magnetic field

Scaling function has a smaller slope than the O(4) model

Negative corrections to scaling observed

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 the Goldstone modes and determine M in the thermodynamic limit on the coexistence line both by extrapolation and by chiral perturbation theory. We compute two critical amplitudes from the scaling behaviours on the coexistence line and on the critical line. In both cases we find negative corrections to scaling. With additional high temperature data we calculate the scaling function and show that it has a smaller slope than that of the O(4) model. For future tests of QCD lattice data we study as well finite-size-scaling functions.