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.
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Communicated by Frank den Hollander.
Submitted: January 6, 2007. Accepted: May 10, 2007.
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Contucci, P., Lebowitz, J. Correlation Inequalities for Spin Glasses. Ann. Henri Poincaré 8, 1461–1467 (2007). https://doi.org/10.1007/s00023-007-0342-8
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DOI: https://doi.org/10.1007/s00023-007-0342-8