Potts Glass on Random Graphs

Details Potts Glass on Random Graphs Potts Glass on Random Graphs

2007-10-17

arxiv.org/abs/0710.3336v2

EPL, 81 (2008) 57005

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 2 figures, 1 table

Scientific paper

10.1209/0295-5075/81/57005

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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