Eur. Phys. J. B 33, 339-346 (2003)
https://doi.org/10.1140/epjb/e2003-00174-7

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

¹ Laboratoire de Physique Théorique de l'École Normale Supérieure (UMR 8549, Unité Mixte de Recherche du Centre National de la Recherche Scientifique et de l' École Normale Supérieure) , 24 rue Lhomond, 75231 Paris Cedex 05, France
² Dipartimento di Fisica and SMC and UdR1 of INFM Università di Roma “La Sapienza” Piazzale Aldo Moro 2, 00185 Roma, Italy

Corresponding author: ^a Federico.Ricci@roma1.infn.it

Received: 10 February 2003
Published online: 20 June 2003

Abstract

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.