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Central Limit Theorems for the Energy Density in the Sherrington-Kirkpatrick Model

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Abstract

In this paper we consider central limit theorems for various macroscopic observables in the high temperature region of the Sherrington-Kirkpatrick spin glass model. With a particular focus on obtaining a quenched central limit theorem for the energy density of the system with non-zero external field, we show how to combine the mean field cavity method with Stein’s method in the quenched regime. The result for the energy density extends the corresponding result of Comets and Neveu in the case of zero external field.

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Authors and Affiliations

  1. Department of Statistics, University of California at Berkeley, 367 Evans Hall #3860, Berkeley, CA, 94720-3860, USA

    Sourav Chatterjee

  2. Department of Industrial Engineering, The Technion, 402 Bloomfield Hall, Haifa, 32000, Israel

    Nicholas Crawford

Authors
  1. Sourav Chatterjee
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  2. Nicholas Crawford
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Correspondence to Nicholas Crawford.

Additional information

S. Chatterjee was supported by a Sloan Research Fellowship and NSF grant DMS 0707054.

N. Crawford was supported in part by DOD ONR grant N0014-07-1-05-06 and at the Technion by an Marilyn and Michael Winer Fellowship.

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Chatterjee, S., Crawford, N. Central Limit Theorems for the Energy Density in the Sherrington-Kirkpatrick Model. J Stat Phys 137, 639–666 (2009). https://doi.org/10.1007/s10955-009-9865-3

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  • DOI: https://doi.org/10.1007/s10955-009-9865-3

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