Swendsen-Wang dynamics for the ferromagnetic Ising model with external fields

被引：0

作者：

Feng, Weiming ^{[1
]}

Guo, Heng ^{[1
]}

Wang, Jiaheng ^{[1
]}

机构：

[1] Univ Edinburgh, Sch Informat, Informat Forum, Edinburgh EH8 9AB, Scotland

来源：

INFORMATION AND COMPUTATION | 2023年 / 294卷

基金：

欧洲研究理事会;

关键词：

Ising model; Random cluster model; Markov chain; Mixing time; Swendsen-Wang dynamics; Holographic transformation; COMPLEXITY;

D O I：

10.1016/j.ic.2023.105066

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world and the random cluster model. Through this new viewpoint, we show:(1) polynomial mixing time bounds for Swendsen-Wang dynamics and (edge-flipping) Glauber dynamics of the random cluster model, generalising the bounds and simplify-ing the proofs for the no-field case by Guo and Jerrum (2018);(2) near linear mixing time for the two dynamics above if the maximum degree is bounded and all fields are (consistent and) bounded away from 1.& COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

引用

页数：34

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