• Corpus ID: 220514263

Entropy decay in the Swendsen-Wang dynamics

  title={Entropy decay in the Swendsen-Wang dynamics},
  author={Antonio Blanca and Pietro Caputo and Daniela Parisi and Alistair Sinclair and Eric Vigoda},
  journal={arXiv: Probability},
We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ${\mathbb Z}^d$. This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is non-local, i.e., it changes the entire configuration in one step. We prove that, whenever strong spatial mixing (SSM) holds, the mixing time on any $n$-vertex cube of ${\mathbb Z}^d$ is $O(\log n)$, improving on the previous best known bound of $O(n)$. SSM is… 

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