Swendsen-Wang dynamics for the ferromagnetic Ising model with external fields
Data Structures and Algorithms
2022-07-19 v2 Probability
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 .
Keywords
Cite
@article{arxiv.2205.01985,
title = {Swendsen-Wang dynamics for the ferromagnetic Ising model with external fields},
author = {Weiming Feng and Heng Guo and Jiaheng Wang},
journal= {arXiv preprint arXiv:2205.01985},
year = {2022}
}
Comments
Major revision and new results