Critical behavior of the planar magnet model in three dimensions

TL;DR

This study investigates the critical behavior of a three-dimensional planar magnet model using advanced Monte Carlo simulations, revealing its universality class and critical exponents through finite-size scaling analysis.

Contribution

The paper introduces a hybrid Monte Carlo approach to accurately determine the critical temperature and exponents of the 3D planar magnet model, highlighting its universality with the XY model.

Findings

Critical temperature significantly differs from the XY model.

Critical exponents are accurately determined: ν=0.670(7), γ/ν=1.9696(37), β/ν=0.515(2).

Model belongs to the XY universality class.

Abstract

We use a hybrid Monte Carlo algorithm in which a single-cluster update is combined with the over-relaxation and Metropolis spin re-orientation algorithm. Periodic boundary conditions were applied in all directions. We have calculated the fourth-order cumulant in finite size lattices using the single-histogram re-weighting method. Using finite-size scaling theory, we obtained the critical temperature which is very different from that of the usual XY model. At the critical temperature, we calculated the susceptibility and the magnetization on lattices of size up to $42^3$. Using finite-size scaling theory we accurately determine the critical exponents of the model and find that $\nu$=0.670(7), $\gamma/\nu$=1.9696(37), and $\beta/\nu$=0.515(2). Thus, we conclude that the model belongs to the same universality class with the XY model, as expected.