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.
On the other hand, we can choose β >0 large enough, such that H ′ β,0,p( 1 2 ) > tanh−1(wp) > 0, which would then imply that H ′ β,0,p(a2(β)) > tanh−1(wp)
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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.