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

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 c...

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Bibliographic Details
Published in:Journal of statistical physics 2009-07, Vol.136 (2), p.205-230
Main Authors: Korada, Satish Babu, Macris, Nicolas
Format: Article
Language:English
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Summary: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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-009-9781-6