Finite-Size Scaling Study of the Three-Dimensional Classical Heisenberg Model

TL;DR

This study employs advanced Monte Carlo simulations and finite-size scaling to accurately estimate critical parameters of the 3D classical Heisenberg model, improving precision and reducing systematic errors.

Contribution

It introduces optimized algorithms and analysis techniques enabling larger lattice simulations and more precise critical point estimations.

Findings

Accurate critical temperature and exponents determined

Reduced critical slowing down observed at phase transition

Enhanced control over finite-size effects

Abstract

We use the single-cluster Monte Carlo update algorithm to simulate the three-dimensional classical Heisenberg model in the critical region on simple cubic lattices of size $L^3$ with $L=12, 16, 20, 24, 32, 40$, and $48$. By means of finite-size scaling analyses we compute high-precision estimates of the critical temperature and the critical exponents, using extensively histogram reweighting and optimization techniques. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.