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Large deviations in spin-glass ground-state energies

A. Andreanov·F. Barbieri·O. C. Martin
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Abstract

The ground-state energy E_0 of a spin glass is an example of an extreme statistic. We consider the large deviations of this energy for a variety of models when the number of spins N goes to infinity. In most cases, the behavior can be understood qualitatively, in particular with the help of semi-analytical results for hierarchical lattices. Particular attention is paid to the Sherrington-Kirkpatrick model; after comparing to the Tracy-Widom distribution which follows from the spherical approximation, we find that the large deviations give rise to non-trivial scaling laws with N.

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A. Andreanov, F. Barbieri, O. C. Martin. 2004-08-03. Large deviations in spin-glass ground-state energies. https://doi.org/10.1140/epjb%2Fe2004-00329-0

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