Some Observations for Mean-Field Spin Glass Models

Abstract

We obtain bounds to show that the pressure of a two-body, mean-field spin glass is a Lipschitz function of the underlying distribution of the random coupling constants, with respect to a particular semi-norm. This allows us to re-derive a result of Carmona and Hu, on the universality of the SK model, by a different proof, and to generalize this result to the Viana-Bray model. We also prove another bound, suitable when the coupling constants are not independent, which is what is necessary if one wants to consider ``canonical'' instead of ``grand canonical'' versions of the SK and Viana-Bray models. Finally, we review Viana-Bray type models, using the language of L\'evy processes, which is natural in this context.