A field-theoretical approach to the spin glass transition: models with long but finite interaction range

Abstract

We study spin glasses with Kac type interaction potential for small but finite inverse interaction range $\gamma$. Using the theoretical setup of coupled replicas, through the replica method we argue that the probability of overlap profiles can be expressed for small $\gamma$ through a large-deviation functional. This result is supported by rigorous arguments, showing that the large-deviation functional provides at least upper bounds for the probability. Finally we analyze the rate function, in the vicinity of the critical point $T_c=1$ of mean field theory, and we study the free energy cost of overlap interfaces, assuming the validity of a gradient expansion for the rate functional.

23 pages

References in corpus (4)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• An Extended Variational Principle for the SK Spin-Glass Model
• The Kac limit for finite-range spin glasses
• Finite-range spin glasses in the Kac limit: free energy and local observables

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• A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models
• Spin glass models with Kac interactions
• A simple one dimensional glassy Kac model