2 problems

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General-graph extension of the critical Swendsen–Wang mixing bound
Consider the zero-field Ising model on a graph with $n$ vertices, and let the Swendsen–Wang dynamics be the associated Markov chain. At criticality on complete graphs, its mixing t…
Conjectureopenising-model mixing-times swendsen-wangarXiv posted 3 days ago
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Logarithmic mixing conjecture for Swendsen–Wang dynamics in nonzero external field
Consider the ferromagnetic Ising model, namely the two-spin system with edge activities $\beta=\gamma>1$ , on a graph with $n$ vertices, and let $lambda$ denote its external field.…
Conjectureopenising-model mixing-times swendsen-wangarXiv posted 3 days ago

General-graph extension of the critical Swendsen–Wang mixing bound