Correlation Inequalities for Spin Glasses

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.

Cited by in corpus (2)

• Lack of monotonicity in spin glass correlation functions
• Dilution Robustness for Mean Field Ferromagnets