Mean-field solution of the Potts glass near the transition temperature to the ordered phase

Details Mean-field solution of the Potts glass near the transition temperature to the ordered phase Mean-field solution of the Potts glass near the transition temperature to the ordered phase

2011-05-19

arxiv.org/abs/1105.3860v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, no figures

Scientific paper

We expand asymptotically mean-field solutions of the $p<4$ Potts glass with various levels of replica-symmetry breaking below the transition temperature to the glassy phase. We find that the ordered phase is degenerate and solutions with one hierarchy of spin replicas and with the full continuous replica-symmetry breaking coexist for $p> p^{*} \approx 2.82$. The latter emerges immediately with the instability of the replica-symmetric one. Apart from these two solutions there exists also a succession of unstable states converging to the solution with the continuous replica-symmetry breaking that is marginally stable and has the highest free energy.

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