High precision single-cluster Monte Carlo measurement of the critical exponents of the classical 3D Heisenberg model

TL;DR

This paper presents high-precision Monte Carlo measurements of critical exponents for the 3D Heisenberg model, utilizing advanced techniques to reduce errors and simulate larger lattices near the phase transition.

Contribution

It introduces a novel approach combining histogram reweighting and optimization to accurately determine critical exponents on larger lattices than previous studies.

Findings

Accurate estimates of critical exponents $ u, eta/ u, ext{and}\, ext{eta}$.

Reduced critical slowing down at phase transition enabling larger lattice simulations.

Enhanced control over systematic errors in finite-size scaling analysis.

Abstract

We report measurements of the critical exponents of the classical three-dimensional Heisenberg model on simple cubic lattices of size $L^3$ with $L$ = 12, 16, 20, 24, 32, 40, and 48. The data was obtained from a few long single-cluster Monte Carlo simulations near the phase transition. We compute high precision estimates of the critical coupling $K_c$, Binder's parameter $U^* and the critical exponents $\nu,\beta / \nu, \eta$, and $\alpha / \nu$, using extensively histogram reweighting and optimization techniques that allow us to keep control over the statistical errors. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition as compared to local update algorithms. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.