Correlation Inequalities for Spin Glasses

Pierluigi Contucci, Joel Lebowitz

Published 2006-12-14Version 1

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.