Two models of spin glasses -- Ising versus Heisenberg

TL;DR

This paper reviews recent numerical studies comparing Ising and Heisenberg spin glasses, focusing on phase transitions, critical properties, and the nature of ordered states, with implications for experimental observations.

Contribution

It provides a comparative analysis of the ordering phenomena in 3D Ising and Heisenberg spin glasses, highlighting differences and similarities in their critical behaviors and phase transitions.

Findings

Different critical behaviors observed in Ising and Heisenberg models.

Evidence of possible replica-symmetry breaking in one or both models.

Contrasts in responses to applied magnetic fields.

Abstract

Brief review is given on recent numerical research of the ordering of two typical models of spin glasses (SGs), the three-dimensional (3D) Ising SG and the 3D Heisenberg SG models. Particular attention is paid to the questions of whether there is a thermodynamic transition in zero field, what are the associated critical properties, what is the nature of the ordered state, particularly of a possible replica-symmetry breaking, and whether there is a thermodynamic transition in applied fields. The properties of the two models are contrasted, and possible relation to experiments is discussed.