Affiliation:
1. Department of Mathematics Courant Institute of Mathematical Sciences New York University New York USA
2. Department of Statistics and Actuarial Science and Department of Applied Mathematics University of Waterloo Waterloo Ontario USA
Abstract
AbstractOur goal in this work is to better understand the relationship between replica symmetry breaking, shattering, and metastability. To this end, we study the static and dynamic behaviour of spherical pure p‐spin glasses above the replica symmetry breaking temperature . In this regime, we find that there are at least two distinct temperatures related to non‐trivial behaviour. First we prove that there is a regime of temperatures in which the spherical p‐spin model exhibits a shattering phase. Our results holds in a regime above but near . We then find that metastable states exist up to an even higher temperature as predicted by Barrat–Burioni–Mézard which is expected to be higher than the phase boundary for the shattering phase . We develop this work by first developing a Thouless–Anderson–Palmer decomposition which builds on the work of Subag. We then present a series of questions and conjectures regarding the sharp phase boundaries for shattering and slow mixing.
Funder
Natural Sciences and Engineering Research Council of Canada
Subject
Applied Mathematics,General Mathematics