Ordered vs Disordered States of the Random-Field Model in Three Dimensions

TL;DR

This study numerically explores the glassy behavior and stability of three-dimensional random-field models with different spin components, revealing distinct singularities and disordering mechanisms.

Contribution

It provides a comparative numerical analysis of 3D random-field models with two and three spin components, highlighting the role of vortex loops and hedgehogs in stability.

Findings

Different stability behaviors for 2- and 3-component models.

Identification of vortex loops and hedgehogs as key singularities.

Insights into disordering mechanisms via Imry-Ma argument.

Abstract

We report numerical investigation of the glassy behavior of random-field exchange models in three dimensions. Correlation of energy with the magnetization for different numbers of spin components has been studied. There is a profound difference between the models with two and three spin components with respect to the stability of the magnetized state due to the different kinds of singularities: vortex loops and hedgehogs, respectively. Memory effects pertinent to such states have been investigated. Insight into the mechanism of the large-scale disordering is provided by numerically implementing the Imry-Ma argument in which the spins follow the random field averaged over correlated volumes. Thermal stability of the magnetized states is investigated by the Monte Carlo method.