Optimal Mixing Time for the Ising Model in the Uniqueness Regime

11/04/2021

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by   Xiaoyu Chen, et al.

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We prove an optimal O(n log n) mixing time of the Glauber dynamics for the Ising models with edge activity β∈(Δ-2/Δ, Δ/Δ-2). This mixing time bound holds even if the maximum degree Δ is unbounded. We refine the boosting technique developed in [CFYZ21], and prove a new boosting theorem by utilizing the entropic independence defined in [AJK+21]. The theorem relates the modified log-Sobolev (MLS) constant of the Glauber dynamics for a near-critical Ising model to that for an Ising model in a sub-critical regime.