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Exponential Control of Overlap in the Replica Method for p-Spin Sherrington-Kirkpatrick Model

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In Talagrand (J. Stat. Phys. 126(4–5):837–894, 2007) the large deviations limit \(\lim_{N\to\infty}(Na)^{-1}\log \mathbb {E}Z_{N}^{a}\) for the moments of the partition function Z N in the Sherrington-Kirkpatrick model (Sherrington and Kirkpatrick in Phys. Rev. Lett. 35:1792–1796, 1972) was computed for all real a≥0. For a≥1 this result extends the classical physicist’s replica method that corresponds to integer values of a. We give a new proof for a≥1 in the case of the pure p-spin SK model that provides a strong exponential control of the overlap.

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  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    Dmitry Panchenko

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  1. Dmitry Panchenko
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Correspondence to Dmitry Panchenko.

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This work is partially supported by NSF grant.

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Panchenko, D. Exponential Control of Overlap in the Replica Method for p-Spin Sherrington-Kirkpatrick Model. J Stat Phys 130, 831–842 (2008). https://doi.org/10.1007/s10955-007-9463-1

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  • DOI: https://doi.org/10.1007/s10955-007-9463-1

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