Critical Behavior of the Three-Dimensional Random Anisotropy Heisenberg Model

TL;DR

This study investigates the critical phenomena of the 3D random anisotropy Heisenberg model through numerical simulations, revealing universality in anisotropic disorder and complex phase transitions including spin glass behavior in isotropic disorder.

Contribution

It provides new insights into the critical behavior and phase transitions of the 3D random anisotropy Heisenberg model with different disorder types and strengths.

Findings

Universality in critical exponents for anisotropic disorder

Two phase transitions in isotropic disorder merging at larger lattices

Evidence of a spin glass phase transition in isotropic disorder

Abstract

We have studied the critical properties of the three-dimensional random anisotropy Heisenberg model by means of numerical simulations using the Parallel Tempering method. We have simulated the model with two different disorder distributions, cubic and isotropic ones, with two different {anisotropy} strengths for each disorder class. For the case of the anisotropic disorder, we have found evidences of universality by finding critical exponents and universal dimensionless ratios independent of the strength of the disorder. In the case of isotropic disorder distribution the situation is very involved: we have found two phase transitions in the magnetization channel which are merging for larger lattices remaining a zero magnetization low temperature phase. Studying this region using a spin glass order parameter we have found evidences for a spin glass phase transition. We have estimated effective critical exponents for the spin glass phase transition for the different values of the strength of the isotropic disorder, discussing the cross-over regime.