Lower bound on the mixing time of $p$-spin glasses

TL;DR

This paper proves that Glauber dynamics for p-spin glasses exhibits exponential slow mixing at certain low temperatures, using energy landscape analysis and bottleneck bounds.

Contribution

It introduces a new analysis of the energy landscape to establish exponential mixing time lower bounds for p-spin glasses at specific temperature regimes.

Findings

Glauber dynamics mixes exponentially slowly at high inverse temperatures for large p

Energy landscape analysis reveals bottlenecks causing slow mixing

Provides rigorous bounds on mixing times in p-spin glass models

Abstract

We show that Glauber dynamics for $ p$-spin glass mixes exponentially slowly at inverse temperatures larger than a constant times $ \ln (p)/p $ for large enough $ p $. This is done by analyzing the energy landscape using Gaussian decompositions and establishing a bottleneck bound.