Spin glasses and percolation

TL;DR

This paper reviews the application of percolation theory to spin glasses, highlighting the challenges and recent advances in understanding phase transitions in frustrated disordered systems.

Contribution

It provides an overview of current methods and open questions in applying percolation concepts to spin glasses and frustrated systems.

Findings

Percolation clusters of aligned spins do not signal phase transitions in spin glasses.

Recent advances have improved understanding of disorder and frustration effects.

Open questions remain about defining meaningful percolation clusters in these systems.

Abstract

The description of thermodynamic phase transitions in terms of percolation transitions of suitably defined clusters has a long tradition and boasts a number of important successes, the most prominent ones being in ferromagnetic lattice models. Spin glasses and other frustrated systems are not among them as the clusters of aligned spins usually considered in this context start to percolate in the disordered phase and hence fail to indicate the onset of ordering. In this mini-review we provide an overview of the state of the art in this field, including recent advances, and outline the main open questions in the area.