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Large deviations in spin-glass ground-state energies

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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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Authors and Affiliations

  1. Laboratoire de Physique Théorique et Modéles Statistiques, bâtiment 100, Université Paris-Sud, 91405, Orsay, France

    A. Andreanov, F. Barbieri & O. C. Martin

Authors
  1. A. Andreanov
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  2. F. Barbieri
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  3. O. C. Martin
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Corresponding author

Correspondence to O. C. Martin.

Additional information

Received: 2 August 2004, Published online: 21 October 2004

PACS:

2.50.-r Probability theory, stochastic processes, and statistics - 05.50. + q Lattice theory and statistics - 75.10.Nr Spin-glass models

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Andreanov, A., Barbieri, F. & Martin, O.C. Large deviations in spin-glass ground-state energies. Eur. Phys. J. B 41, 365–375 (2004). https://doi.org/10.1140/epjb/e2004-00329-0

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  • DOI: https://doi.org/10.1140/epjb/e2004-00329-0

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