Large deviations in spin-glass ground-state energies

Details Large deviations in spin-glass ground-state energies Large deviations in spin-glass ground-state energies

2003-07-29

arxiv.org/abs/cond-mat/0307709v2

Eur. Phys. J. B. 41 (3), 365 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, 12 figures, extended discussion, clarifications and references

Scientific paper

10.1140/epjb/e2004-00329-0

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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