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Swendsen-Wang dynamics for the ferromagnetic Ising model with external fields
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abstract
We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world and the random cluster model. Through this new viewpoint, we show: (1) polynomial mixing time bounds for Swendsen-Wang dynamics and (edge-flipping) Glauber dynamics of the random cluster model, generalising the bounds and simplifying the proofs for the no-field case by Guo and Jerrum (2018); (2) near linear mixing time for the two dynamics above if the maximum degree is bounded and all fields are (consistent and) bounded away from $1$.
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Efficient Parallel Ising Samplers via Localization Schemes
Provides the first RNC-class parallel samplers for ferromagnetic Ising models with fields and for Ising models with interaction norm below 1, using localization schemes.
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