Volume 81, Number 5, March 2008
|Number of page(s)||6|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|Published online||04 February 2008|
Potts glass on random graphs
PCT, UMR 7083 CNRS-ESPCI - 10 rue Vauquelin, 75231 Paris, France
2 Université Paris-Sud, LPTMS, UMR8626 - Bât. 100, Université Paris-Sud, 91405 Orsay cedex, France
3 CNRS, LPTMS, UMR8626 - Bât. 100, Université Paris-Sud, 91405 Orsay cedex, France
Accepted: 4 January 2008
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.
PACS: 75.10.Nr – Spin-glass and other random models / 89.20.Ff – Computer science and technology
© EPLA, 2008
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.