Scaling Behavior of the Heisenberg Model in Three Dimensions

TL;DR

This paper presents extensive numerical simulations of the 3D Heisenberg model, analyzing its critical and ferromagnetic phases through Lee-Yang zeros to understand scaling behavior and Goldstone modes.

Contribution

It provides a comprehensive Lee-Yang analysis of the 3D Heisenberg model, including corrections to scaling and confirmation of critical exponents.

Findings

Finite-size scaling of Lee-Yang zeros reveals Goldstone mode effects.

Confirmed recent estimates of critical exponents.

Analyzed scaling behavior in both critical and ferromagnetic phases.

Abstract

We report on extensive numerical simulations of the three-dimensional Heisenberg model and its analysis through finite-size scaling of Lee-Yang zeros. Besides the critical regime, we also investigate scaling in the ferromagnetic phase. We show that, in this case of broken symmetry, the corrections to scaling contain information on the Goldstone modes. We present a comprehensive Lee-Yang analysis, including the density of zeros and confirm recent numerical estimates for critical exponents.