Potts Glass on Random Graphs

Abstract : We solve the q-state Potts model with anti-ferromagnetic interactions on large random lattices of finite coordination. Due to the frustration induced by the large loops and to the local tree-like structure of the lattice this model behaves as a mean field spin glass. We use the cavity method to compute the temperature-coordination phase diagram and to determine the location of the dynamic and static glass transitions, and of the Gardner instability. We show that for q>=4 the model possesses a phenomenology similar to the one observed in structural glasses. We also illustrate the links between the positive and the zero-temperature cavity approaches, and discuss the consequences for the coloring of random graphs. In particular we argue that in the colorable region the one-step replica symmetry breaking solution is stable towards more steps of replica symmetry breaking.
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Submitted on : Tuesday, July 22, 2008 - 4:16:20 PM
Last modification on : Thursday, January 11, 2018 - 6:14:29 AM

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  • HAL Id : hal-00304234, version 1
  • ARXIV : 0710.3336

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Florent Krzakala, Lenka Zdeborová. Potts Glass on Random Graphs. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2008, 81, pp.57005. ⟨hal-00304234⟩

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