2007/10/31 by Florent Krzakala, F. Krząkała, Lenka Zdeborová +1 · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Chiral Potts curve #Frustration #Material Dynamics and Properties #Phase diagram #Potts model #Random Matrices and Applications #Random graph #Replica #Replica trick #Spin glass #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1209/0295-5075/81/57005
published as EPL, 81 (2008) 57005 · 6 pages, 2 figures, 1 table
arxiv created 2007/12/12 · openalex publication_date 2008/02/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.