The XY Model and the Three-state Antiferromagnetic Potts model in Three Dimensions: Critical Properties from Fluctuating Boundary Conditions

TL;DR

This study uses Monte Carlo simulations to analyze the critical properties of the 3D XY and antiferromagnetic 3-state Potts models, confirming their shared universality class through boundary condition effects.

Contribution

It provides new Monte Carlo-based estimates of critical temperature and exponent nu for both models using boundary condition differences.

Findings

Critical temperature and nu values are consistent with recent studies.

Both models belong to the same universality class.

Finite-size scaling of free energy differences supports universality.

Abstract

We present the results of a Monte Carlo study of the three-dimensional XY model and the three-dimensional antiferromagnetic three-state Potts model. In both cases we compute the difference in the free energies of a system with periodic and a system with antiperiodic boundary conditions in the neighbourhood of the critical coupling. From the finite-size scaling behaviour of this quantity we extract values for the critical temperature and the critical exponent nu that are compatible with recent high statistics Monte Carlo studies of the models. The results for the free energy difference at the critical temperature and for the exponent nu confirm that both models belong to the same universality class.