Shattering versus metastability in spin glasses

Our 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 Ts$T_{s}$. 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 Ts$T_s$. We then find that metastable states exist up to an even higher temperature TBBM$T_{BBM}$ as predicted by Barrat-Burioni-Mezard which is expected to be higher than the phase boundary for the shattering phase Td

Automated summary

The objective of this study is to gain a better understanding of the relationship between replica symmetry breaking, shattering, and metastability. To achieve this, we investigated the static and dynamic behavior of spherical pure p-spin glasses above the replica symmetry breaking temperature Ts. Within this range, we identified at least two distinct temperatures associated with non-trivial behavior. Firstly, we demonstrated the existence of a shattering phase in the spherical p-spin model within a temperature regime above but close to Ts. Additionally, we found that metastable states persist up to a higher temperature TBBM, as predicted by Barrat-Burioni-Mezard, which is expected to be higher than the phase boundary for the shattering phase Td.