Session S04 - Random Walks and Related Topics

Monday, July 19, 16:40 ~ 17:10 UTC-3

The shattering phase and metastability for spin glasses

Gerard BEN AROUS

Courant Institute of Mathematical Sciences, New York University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

I will present a recent joint work with Aukosh Jagannath, where we explore 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. We then find that metastable states exist up to an even higher temperature, as predicted by Barrat–Burioni–Mezard, which is expected to be higher than the phase boundary for the shattering phase.

We first develop a Thouless–Anderson–Palmer decomposition which builds on the recent work of Subag. We then present a series of questions and conjectures regarding the sharp phase boundaries for shattering and slow mixing.

Joint work with Aukosh Jagannath (University of Waterloo).

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