Correlation Inequalities for Spin Glasses

Details Correlation Inequalities for Spin Glasses Correlation Inequalities for Spin Glasses

2006-12-14

arxiv.org/abs/cond-mat/0612371v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1007/s00023-007-0342-8

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.

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