Electronic ISBN:  9781470418953 
Product Code:  MEMO/232/1092.E 
List Price:  $65.00 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 232; 2014; 84 ppMSC: Primary 60; Secondary 82;
The SwendsenWang dynamics is a Markov chain widely used by physicists to sample from the BoltzmannGibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the complete graph \(K_n\) the mixing time of the chain is at most \(O(\sqrt{n})\) for all noncritical temperatures.
In this paper the authors show that the mixing time is \(\Theta(1)\) in high temperatures, \(\Theta(\log n)\) in low temperatures and \(\Theta(n^{1/4})\) at criticality. They also provide an upper bound of \(O(\log n)\) for SwendsenWang dynamics for the \(q\)state ferromagnetic Potts model on any tree of \(n\) vertices. 
Table of Contents

Chapters

1. Introduction

2. Statement of the results

3. Mixing time preliminaries

4. Outline of the proof of Theorem

5. Random graph estimates

6. Supercritical case

7. Subcritical case

8. Critical Case

9. Fast mixing of the SwendsenWang process on trees

Acknowledgements


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The SwendsenWang dynamics is a Markov chain widely used by physicists to sample from the BoltzmannGibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the complete graph \(K_n\) the mixing time of the chain is at most \(O(\sqrt{n})\) for all noncritical temperatures.
In this paper the authors show that the mixing time is \(\Theta(1)\) in high temperatures, \(\Theta(\log n)\) in low temperatures and \(\Theta(n^{1/4})\) at criticality. They also provide an upper bound of \(O(\log n)\) for SwendsenWang dynamics for the \(q\)state ferromagnetic Potts model on any tree of \(n\) vertices.

Chapters

1. Introduction

2. Statement of the results

3. Mixing time preliminaries

4. Outline of the proof of Theorem

5. Random graph estimates

6. Supercritical case

7. Subcritical case

8. Critical Case

9. Fast mixing of the SwendsenWang process on trees

Acknowledgements