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arXiv · 0710.3336

Potts Glass on Random Graphs

Florent Krzakala·Lenka Zdeborová
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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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Florent Krzakala, Lenka Zdeborová. 2007-12-12. Potts Glass on Random Graphs. https://doi.org/10.1209/0295-5075%2F81%2F57005

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