On the nature of the spin glass transition

TL;DR

This paper explains why two-dimensional Ising spin glasses lack a finite temperature transition by linking their properties to an internal symmetry, and discusses how higher dimensions allow spontaneous symmetry breaking leading to spin glass order.

Contribution

It reveals that the absence of a finite temperature transition in 2D spin glasses is due to an internal symmetry, extending understanding to higher dimensions where symmetry breaking occurs.

Findings

2D spin glasses have a line of RG fixed points linked to an internal symmetry.

No finite temperature transition occurs in 2D due to this symmetry.

Higher dimensions exhibit spontaneous symmetry breaking, leading to a continuous spin glass order parameter.

Abstract

We recently showed that the two-dimensional Ising spin glass allows for a line of renormalization group fixed points which explains properties observed in numerical studies. We observe that this exact result corresponds to enhancement to a one-generator continuous internal symmetry. This finally explains why no finite temperature transition to a spin glass phase is observed in two dimensions. In more than two dimensions, instead, the continuous symmetry can be broken spontaneously and yields a spin glass order parameter which, for fixed temperature and disorder strength, takes continuous values in an interval. Such a feature is shared by the order parameter of the known mean field solution of the model with infinite-range interactions, which corresponds to infinitely many dimensions.