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Some rigorous results on the Sherrington-Kirkpatrick spin glass model

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Abstract

We prove that in the high temperature regime (T/J>1) the deviation of the total free energy of the Sherrington-Kirkpatrick (S-K) spin glass model from the easily computed log Av(Z N ({βJ})) converges in distribution, asN → ∞, to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained.

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Authors and Affiliations

  1. Departments of Mathematics and Physics, Rutgers University, 08903, New Brunswick, NJ, USA

    M. Aizenman, J. L. Lebowitz & D. Ruelle

Authors
  1. M. Aizenman
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  2. J. L. Lebowitz
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  3. D. Ruelle
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Additional information

Communicated by E. Lieb

Dedicated to Walter Thirring on his 60th birthday

Research supported in part by the NSF grant PHY-8605164. Present address: Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012, USA

Research supported in part by the NSF grant DMR 86-12369

On leave from Institut des Hautes Etudes Scientifiques, Bures-Sur-Yvette, France

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Aizenman, M., Lebowitz, J.L. & Ruelle, D. Some rigorous results on the Sherrington-Kirkpatrick spin glass model. Commun.Math. Phys. 112, 3–20 (1987). https://doi.org/10.1007/BF01217677

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  • DOI: https://doi.org/10.1007/BF01217677

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