https://doi.org/10.1140/epjb/e2004-00329-0
Large deviations in spin-glass ground-state energies
Laboratoire de Physique Théorique et Modèles Statistiques,
bâtiment 100, Université Paris-Sud, 91405 Orsay, France
Corresponding author: a martino@ipno.in2p3.fr
Received:
19
September
2003
Revised:
2
August
2004
Published online:
21
October
2004
The ground-state energy E0 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.
PACS: 2.50.-r – Probability theory, stochastic processes, and statistics / 05.50.+q – Lattice theory and statistics / 75.10.Nr – Spin-glass models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004
