Energy exponents and corrections to scaling in Ising spin glasses

Jean-Philippe Bouchaud 1, Florent Krzakala 2, 3, Olivier C. Martin 1, 2

Physical Review B 68 (2003) 224404

We study the probability distribution P(E) of the ground state energy E in various Ising spin glasses. In most models, P(E) seems to become Gaussian with a variance growing as the system's volume V. Exceptions include the Sherrington-Kirkpatrick model (where the variance grows more slowly, perhaps as the square root of the volume), and mean field diluted spin glasses having +/-J couplings. We also find that the corrections to the extensive part of the disorder averaged energy grow as a power of the system size; for finite dimensional lattices, this exponent is equal, within numerical precision, to the domain-wall exponent theta_DW. We also show how a systematic expansion of theta_DW in powers of exp(-d) can be obtained for Migdal-Kadanoff lattices. Some physical arguments are given to rationalize our findings.

  • 1. Service de physique de l'état condensé (SPEC),
    CNRS : URA2464 – CEA : DSM/IRAMIS
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3. Dipartimento di Fisica,
    INFM – SMC – Università degli studi di Roma I - La Sapienza