Thermodynamic Limit for Spin Glasses. Beyond the Annealed Bound

TL;DR

This paper proves the existence of the thermodynamic limit for short-range spin glasses using a correlation inequality, removing the need for the annealed bound assumption, thus broadening the theoretical understanding of spin glass models.

Contribution

It introduces a new proof of the thermodynamic limit for spin glasses that requires weaker conditions than prior methods, specifically without the annealed bound.

Findings

Thermodynamic limit exists for short-range spin glasses.

Weaker hypotheses suffice for the proof.

Correlation inequality is key to the new proof.

Abstract

Using a correlation inequality of Contucci and Lebowitz for spin glasses, we demonstrate existence of the thermodynamic limit for short-ranged spin glasses, under weaker hypotheses than previously available, namely without the assumption of the annealed bound.