Mean-field solution of the Potts glass near the transition temperature to the ordered phase

Abstract

We expand asymptotically mean-field solutions of the $p<4$ Potts glass with various levels of replica-symmetry breaking below the transition temperature to the glassy phase. We find that the ordered phase is degenerate and solutions with one hierarchy of spin replicas and with the full continuous replica-symmetry breaking coexist for $p>p^{\ast }\approx 2.82$. The latter emerges immediately with the instability of the replica-symmetric one. Apart from these two solutions there exists also a succession of unstable states converging to the solution with the continuous replica-symmetry breaking that is marginally stable and has the highest free energy.

11 pages, no figures

References in corpus (6)

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• Full versus first stage replica symmetry breaking in spin glasses
• Potts spin glasses with 3, 4 and 5 states near $T=T_c$: expanding around the replica symmetric solution
• The Parisi formula completed
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Cited by in corpus (7)

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• Continuous and discontinuous transitions in generalized p-spin glass models
• Continuous replica-symmetry breaking in mean-field spin-glass models: Perturbation expansion without the replica trick
• Generalized Sherrington--Kirkpatrick-glass without reflection symmetry
• Orientational glass: full replica symmetry breaking in generalized spin glass-like models without reflection symmetry
• A curious relationship between Potts glass models
• Ergodicity breaking in frustrated disordered systems: Replicas in mean-field spin-glass models