Specific heat and energy for the three-dimensional O(2) model

TL;DR

This study analyzes the critical behavior of the three-dimensional O(2) model near the phase transition, confirming critical parameters and exploring universal amplitude ratios through extensive lattice simulations.

Contribution

It provides precise estimates of critical coupling, universal ratios, and finite size effects for the 3D O(2) model, confirming previous findings and extending understanding of its critical properties.

Findings

Confirmed critical coupling J_c consistent with prior work

Estimated universal values of g_r and xi/L at criticality

Determined the universal amplitude ratio A+/A- and its alpha-dependence

Abstract

We investigate the three-dimensional O(2) model on lattices of size 8^3 to 160^3 close to the critical point at zero magnetic field. We confirm explicitly the value of the critical coupling J_c found by Ballesteros et al. and estimate there the universal values of g_r and xi/L. At the critical point we study the finite size dependencies of the energy density epsilon and the specific heat C. We find that the nonsingular part of the specific heat C_{ns} is linearly dependent on 1/alpha. From the critical behaviour of the specific heat for T not T_c on the largest lattices we determine the universal amplitude ratio A+/A-. The alpha- dependence of this ratio is close to the phenomenological relation A+/A- = 1-4alpha.