For the p-spin Curie-Weiss model, Glauber dynamics has three mixing-time scales determined by the number and curvature of local maxima of a function H, and a restricted version mixes fast even in the slow regime.
By Lemma F.2 in Mukherjee, Son and Bhattacharya (2021), the only p-special point for odd p is ( ˆβp, ˆhp), and the only p-special points for even p are ( ˆβp, ±ˆhp)
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Mixing Phases and Metastability for the Glauber Dynamics on the p-Spin Curie-Weiss Model
For the p-spin Curie-Weiss model, Glauber dynamics has three mixing-time scales determined by the number and curvature of local maxima of a function H, and a restricted version mixes fast even in the slow regime.