Monte Carlo Study of Topological Defects in the 3D Heisenberg Model

TL;DR

This study uses advanced Monte Carlo simulations to analyze topological defects in the 3D Heisenberg model, revealing that defect density derivatives behave like specific heat and do not diverge at the transition, contrary to earlier findings.

Contribution

It provides new evidence that the temperature derivative of defect density remains finite at the transition, challenging previous divergent behavior assumptions, and offers precise critical exponent estimates.

Findings

The derivative of defect density is finite at the transition.

The defect density derivative scales similarly to specific heat.

Accurate estimate of the ratio α/ν from finite-size scaling.

Abstract

We use single-cluster Monte Carlo simulations to study the role of topological defects in the three-dimensional classical Heisenberg model on simple cubic lattices of size up to $80^3$. By applying reweighting techniques to time series generated in the vicinity of the approximate infinite volume transition point $K_c$, we obtain clear evidence that the temperature derivative of the average defect density $d\langle n \rangle/dT$ behaves qualitatively like the specific heat, i.e., both observables are finite in the infinite volume limit. This is in contrast to results by Lau and Dasgupta [{\em Phys. Rev.\/} {\bf B39} (1989) 7212] who extrapolated a divergent behavior of $d\langle n \rangle/dT$ at $K_c$ from simulations on lattices of size up to $16^3$. We obtain weak evidence that $d\langle n \rangle/dT$ scales with the same critical exponent as the specific heat.As a byproduct of our simulations, we obtain a very accurate estimate for the ratio $\alpha/\nu$ of the specific-heat exponent with the correlation-length exponent from a finite-size scaling analysis of the energy.