F. Krząkała and L. Zdeborová 2008 EPL 81 57005 doi:10.1209/0295-5075/81/57005
F. Krząkała1 and L. Zdeborová2,3
Show affiliationsWe 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.
Issue 5 (March 2008)
Received 20 October 2007, accepted for publication 4 January 2008
Published 4 February 2008
F. Krząkała and L. Zdeborová 2008 EPL 81 57005
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