On the nature of the low-temperature phase in discontinuous mean-field spin glasses

Details On the nature of the low-temperature phase in discontinuous mean-field spin glasses On the nature of the low-temperature phase in discontinuous mean-field spin glasses

2003-01-30

arxiv.org/abs/cond-mat/0301591v1

Eur. Phys. J. B 33, 339 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

14 pages, 7 figures

Scientific paper

10.1140/epjb/e2003-00174-7

The low-temperature phase of discontinuous mean-field spin glasses is generally described by a one-step replica symmetry breaking (1RSB) Ansatz. The Gardner transition, i.e. a very-low-temperature phase transition to a full replica symmetry breaking (FRSB) phase, is often regarded as an inessential, and somehow exotic phenomenon. In this paper we show that the metastable states which are relevant for the out-of-equilibrium dynamics of such systems are always in a FRSB phase. The only exceptions are (to the best of our knowledge) the p-spin spherical model and the random energy model (REM). We also discuss the consequences of our results for aging dynamics and for local search algorithms in hard combinatorial problems.

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