带外场的铁磁Ising模型的Swendsen-Wang动力学

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

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引用次数: 1

摘要

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。

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

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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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

期刊介绍： Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as -Biological computation and computational biology- Computational complexity- Computer theorem-proving- Concurrency and distributed process theory- Cryptographic theory- Data base theory- Decision problems in logic- Design and analysis of algorithms- Discrete optimization and mathematical programming- Inductive inference and learning theory- Logic & constraint programming- Program verification & model checking- Probabilistic & Quantum computation- Semantics of programming languages- Symbolic computation, lambda calculus, and rewriting systems- Types and typechecking