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

IF 0.8 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Information and Computation Pub Date : 2023-10-01 DOI:10.1016/j.ic.2023.105066

Weiming Feng, Heng Guo, Jiaheng Wang

引用次数: 1

Abstract

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 simplifying 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.

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带外场的铁磁Ising模型的Swendsen-Wang动力学

我们研究了具有一致外部场的铁磁Ising模型的采样问题，特别是该模型上的Swendsen-Wang动力学。我们引入了一个新的大模型，将两个密切相关的模型统一起来：子图世界和随机聚类模型。通过这一新观点，我们证明了：（1）随机簇模型的Swendsen-Wang动力学和（边缘翻转）Glauber动力学的多项式混合时间界，推广了Guo和Jerrum（2018）对无场情况的边界并简化了证明；（2）如果最大度是有界的并且所有场都（一致的并且）有界远离1，则上述两个动力学的近似线性混合时间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Information and Computation 工程技术-计算机：理论方法

CiteScore

2.30

自引率

0.00%

发文量

119

审稿时长

140 days

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