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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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Published in: | Journal of statistical physics 2009-07, Vol.136 (2), p.205-230 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0022-4715 1572-9613 |
DOI: | 10.1007/s10955-009-9781-6 |