5 research outputs found
Some Observations for Mean-Field Spin Glass Models
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.Comment: 15 pages, minor revision