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High temperature regime for a multidimensional Sherrington–Kirkpatrick model of spin glass
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  • Published: May 1998

High temperature regime for a multidimensional Sherrington–Kirkpatrick model of spin glass

  • Alain Toubol1 

Probability Theory and Related Fields volume 110, pages 497–534 (1998)Cite this article

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Abstract.

Comets and Neveu have initiated in [5] a method to prove convergence of the partition function of disordered systems to a log-normal random variable in the high temperature regime by means of stochastic calculus. We generalize their approach to a multidimensional Sherrington-Kirkpatrick model with an application to the Heisenberg model of uniform spins on a sphere of ℝd, see [9]. The main tool that we use is a truncation of the partition function outside a small neighbourhood of the typical energy path.

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Authors and Affiliations

  1. ENPC-CERMICS, 6/8 av. Blaise Pascal Cite Descartes, Champs-Sur-Marne, F-77455 Marne-la-Vallée Cedex 2, France and Université Paris 7, URA 1321 “Statistique et modèles aléatoires” e-mail: toubol@cermics.enpc.fr, , , , , , FR

    Alain Toubol

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  1. Alain Toubol
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Received: 30 October 1996 / In revised form: 13 October 1997

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Toubol, A. High temperature regime for a multidimensional Sherrington–Kirkpatrick model of spin glass. Probab Theory Relat Fields 110, 497–534 (1998). https://doi.org/10.1007/s004400050157

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  • Issue Date: May 1998

  • DOI: https://doi.org/10.1007/s004400050157

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  • Mathematics Subject Classification (1991): 60K35
  • 82B44
  • 82D30.
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