Critical Behaviour of the 3D XY-Model: A Monte Carlo Study

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior of the 3D XY-model, determining critical coupling and exponents with high precision.

Contribution

It provides new high-precision estimates of the critical coupling and critical exponents for the 3D XY-model using advanced Monte Carlo techniques.

Findings

Critical coupling $eta_c=0.45420(2)$

Critical exponents $rac{eta}{ u}=1.976(6)$ and $ u=0.662(7)$

Accurate measurements of susceptibility and correlation length

Abstract

We present the results of a study of the three-dimensional $XY$-model on a simple cubic lattice using the single cluster updating algorithm combined with improved estimators. We have measured the susceptibility and the correlation length for various couplings in the high temperature phase on lattices of size up to $L=112$. At the transition temperature we studied the fourth-order cumulant and other cumulant-like quantities on lattices of size up to $L=64$. From our numerical data we obtain for the critical coupling $\coup_c=0.45420(2)$, and for the static critical exponents $\gamma /\nu=1.976(6)$ and $\nu=0.662(7)$.