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arXiv · 0707.0031

Some Observations for Mean-Field Spin Glass Models

Shannon Starr·Brigitta Vermesi
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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 Lévy processes, which is natural in this context.

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Shannon Starr, Brigitta Vermesi. 2007-12-23. Some Observations for Mean-Field Spin Glass Models. https://doi.org/10.1007/s11005-008-0224-0

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