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

Silvio Franz·Fabio Lucio Toninelli
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Abstract

We study spin glasses with Kac type interaction potential for small but finite inverse interaction range $γ$. Using the theoretical setup of coupled replicas, through the replica method we argue that the probability of overlap profiles can be expressed for small $γ$ 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.

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Silvio Franz, Fabio Lucio Toninelli. 2005-01-31. A field-theoretical approach to the spin glass transition: models with long but finite interaction range. https://doi.org/10.1088/1742-5468%2F2005%2F01%2Fp01008

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