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Power law of order 1/4 for critical mean field Swendsen-Wang dynamics / Yun Long...[et al.].

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 232, no 1092.Publication details: Providence : American Mathematical Society, 2c014.Description: v, 84 p. ; 26 cmISBN:
  • 9781470409104 (pbk. : acidfree paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Introduction-- 2. Statement of the results-- 3. Mixing time preliminaries-- 4. Outline of the proof of Theorem 2.1-- 5. Random graph estimates-- 6. Supercritical case-- 7. Subcritical case-- 8. Critical case-- 9. Fast mixing of the Swendsen-Wang process on trees-- Acknowledgements-- Bibliography.
Summary: The Swendsen-Wang dynamics is a Markov chain widely used by physicists to sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the complete graph Kn the mixing time of the chain is at most O( O n) for all non-critical temperatures. In this paper the authors show that the mixing time is Q (1) in high temperatures, Q (log n) in low temperatures and Q (n 1/4) at criticality. They also provide an upper bound of O(log n) for Swendsen-Wang dynamics for the q-state ferromagnetic Potts model on any tree of n vertices.
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"Volume 232, number 1092 (fourth of 6 numbers), November 2014."

Includes bibliographical references (pages 83-84).

1. Introduction--
2. Statement of the results--
3. Mixing time preliminaries--
4. Outline of the proof of Theorem 2.1--
5. Random graph estimates--
6. Supercritical case--
7. Subcritical case--
8. Critical case--
9. Fast mixing of the Swendsen-Wang process on trees-- Acknowledgements--
Bibliography.

The Swendsen-Wang dynamics is a Markov chain widely used by physicists to sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the complete graph Kn the mixing time of the chain is at most O( O n) for all non-critical temperatures. In this paper the authors show that the mixing time is Q (1) in high temperatures, Q (log n) in low temperatures and Q (n 1/4) at criticality. They also provide an upper bound of O(log n) for Swendsen-Wang dynamics for the q-state ferromagnetic Potts model on any tree of n vertices.

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