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

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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].

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References

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Authors and Affiliations

  1. UFR de Mathematiques, Université Paris 7, case 7012, F-75251, CNRS 756 and 1321, Paris Cedex 05, France

    F. Comets

  2. Ecole Polytechnique, CMAP, F-91128, CNRS 756, Palaiseau Cedex, France

    J. Neveu

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  1. F. Comets
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  2. J. Neveu
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Communicated by D. C. Brydges

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Comets, F., Neveu, J. The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: The high temperature case. Commun.Math. Phys. 166, 549–564 (1995). https://doi.org/10.1007/BF02099887

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  • DOI: https://doi.org/10.1007/BF02099887

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