Critical exponents of a three dimensional O(4) spin model

TL;DR

This study uses Monte Carlo simulations to accurately determine the critical exponents of the 3D O(4) spin model, relevant for understanding phase transitions in QCD, and confirms their consistency with theoretical predictions.

Contribution

It provides precise non-perturbative estimates of critical exponents for the 3D O(4) model using advanced simulation techniques, improving accuracy over previous methods.

Findings

Critical exponents agree with $4- ext{epsilon}$ expansion results.

Estimated critical temperature $eta_c=0.9360(1)$.

Errors in exponents are reduced by about half.

Abstract

By Monte Carlo simulation we study the critical exponents governing the transition of the three-dimensional classical O(4) Heisenberg model, which is considered to be in the same universality class as the finite-temperature QCD with massless two flavors. We use the single cluster algorithm and the histogram reweighting technique to obtain observables at the critical temperature. After estimating an accurate value of the inverse critical temperature $\Kc=0.9360(1)$, we make non-perturbative estimates for various critical exponents by finite-size scaling analysis. They are in excellent agreement with those obtained with the $4-\epsilon$ expansion method with errors reduced to about halves of them.