Rapid mixing of fixed-temperature Glauber dynamics for the high-temperature SK model

Prove that the canonical fixed-temperature Glauber dynamics for the Sherrington–Kirkpatrick model mixes rapidly throughout the high-temperature regime 0 ≤ β < 1.

Background

The paper distinguishes simulated annealing from the standard Glauber dynamics run at a fixed inverse temperature. Although the paper establishes efficient sampling for simulated annealing when β < 1, it does not resolve rapid mixing from a generic initialization for the fixed-temperature chain.

The unresolved fixed-temperature question is a central motivation for studying annealing: the annealing schedule gradually increases the inverse temperature and uses weak Poincaré inequalities to transfer sampling guarantees across temperatures.