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2015
Springer

Swendsen-Wang Algorithm on the Mean-Field Potts Model

5 years 7 months ago
Swendsen-Wang Algorithm on the Mean-Field Potts Model
We study the q-state ferromagnetic Potts model on the n-vertex complete graph known as the mean-field (Curie-Weiss) model. We analyze the Swendsen-Wang algorithm which is a Markov chain that utilizes the random cluster representation for the ferromagnetic Potts model to recolor large sets of vertices in one step and potentially overcomes obstacles that inhibit single-site Glauber dynamics. The case q = 2 (the Swendsen-Wang algorithm for the ferromagnetic Ising model) undergoes a slow-down at the uniqueness/non-uniqueness critical temperature for the infinite ∆-regular tree ([16]) but yet still has polynomial mixing time at all (inverse) temperatures β > 0 ([7]). In contrast for q ≥ 3 there are two critical temperatures 0 < βu < βrc that are relevant, these two critical points relate to phase transitions in the infinite tree. We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the nvertex complete graph satisfies: (i) O(...
Andreas Galanis, Daniel Stefankovic, Eric Vigoda
Added 16 Apr 2016
Updated 16 Apr 2016
Type Journal
Year 2015
Where APPROX
Authors Andreas Galanis, Daniel Stefankovic, Eric Vigoda
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