Communications in Mathematical Physics

, Volume 166, Issue 3, pp 549–564 | Cite as

The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: The high temperature case

  • F. Comets
  • J. Neveu
Article

Abstract

We study the fluctuations of free energy, energy and entropy in the high temperature regime for the Sherrington-Kirkpatrick model of spin glasses. We introduce here a new dynamical method with the help of brownian motions and continuous martingales indexed by the square root of the inverse temperature as parameter, thus formulating the thermodynamic formalism in terms of random processes. The well established technique of stochastic calculus leads us naturally to prove that these fluctuations are simple gaussian processes with independent increments, a generalization of a result proved by Aizenman, Lebowitz and Ruelle [1].

Keywords

Entropy Neural Network Free Energy Brownian Motion Random Process 

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References

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • F. Comets
    • 1
  • J. Neveu
    • 2
  1. 1.UFR de MathematiquesUniversité Paris 7Paris Cedex 05France
  2. 2.Ecole PolytechniqueCMAPPalaiseau CedexFrance

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