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

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

2004-08-12

arxiv.org/abs/cond-mat/0408270v2

J. Stat. Mech.: Theor. Exp. (2005) P01008

Physics

Condensed Matter

Disordered Systems and Neural Networks

23 pages

Scientific paper

10.1088/1742-5468/2005/01/P01008

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.

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