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Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph

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Abstract

We consider a gauge symmetric version of the p-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra (Fields Inst. Commun. 30:161, 2001) to rigorously compute the free energy. In the case of pairwise interactions (p=2), where we have a gauge symmetric version of the Sherrington-Kirkpatrick model, we get the free energy and magnetization for all values of external parameters. Our analysis also works for even p≥4 except in a range of parameters surrounding the phase transition line, and for odd p≥3 in a more restricted region. We also obtain concentration estimates for the magnetization and overlap parameter that play a crucial role in the proofs for odd p and justify the absence of replica symmetry breaking. Our initial motivation for considering this model came from problems related to communication over a noisy channel, and is briefly explained.

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Authors and Affiliations

  1. Communication Theory Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), LTHC, IC, Station 14, 1015, Lausanne, Switzerland

    Satish Babu Korada & Nicolas Macris

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  1. Satish Babu Korada
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  2. Nicolas Macris
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Correspondence to Nicolas Macris.

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Korada, S.B., Macris, N. Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph. J Stat Phys 136, 205–230 (2009). https://doi.org/10.1007/s10955-009-9781-6

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  • DOI: https://doi.org/10.1007/s10955-009-9781-6

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