Correlation Inequalities for Spin Glasses

TL;DR

This paper establishes a correlation inequality for spin glasses with symmetric random interactions, leading to monotonicity of pressure and existence of thermodynamic limits, advancing understanding of their statistical properties.

Contribution

It introduces a new correlation inequality for spin glasses with symmetric quenched interactions, providing key monotonicity results and bounds on surface pressure.

Findings

Proves a correlation inequality for symmetric spin glasses.

Shows monotonicity of pressure with interaction strength.

Establishes existence of thermodynamic limits.

Abstract

We prove a correlation type inequality for spin systems with quenched symmetric random interactions. This gives monotonicity of the pressure with respect to the strength of the interaction for a class of spin glass models. Consequences include existence of the thermodynamic limit for the pressure and bounds on the surface pressure. We also describe other conjectured inequalities for such systems.