No Percolation in low temperature spin glass

TL;DR

This paper proves that at low temperatures, the Edwards-Anderson Ising Spin Glass model's unsatisfied edges form only finite clusters, indicating no percolation occurs in the system.

Contribution

It establishes the non-percolation of unsatisfied edges in the low-temperature regime of the Edwards-Anderson spin glass model, a novel result in spin glass theory.

Findings

Unsatisfied edges form finite components at low temperatures

Percolation of unsatisfied edges does not occur in the model

Results hold for almost every spin configuration

Abstract

We consider the Edwards-Anderson Ising Spin Glass model for non negative temperatures T: We define the natural notion of Boltzmann- Gibbs measure for the Edwards-Anderson spin glass at a given temperature, and of unsatisfied edges. We prove that for low enough temperatures, in almost every spin configuration the graph formed by the unsatisfied edges is made of finite connected components. In other words, the unsatisfied edges do not percolate.