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

Weiming Feng, Heng Guo, Jiaheng Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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-fieldcase 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.
Original languageEnglish
Article number105066
Pages (from-to)1-34
JournalInformation and Computation
Early online date3 Jul 2023
Publication statusPublished - 12 Jul 2023

Keywords / Materials (for Non-textual outputs)

  • Ising model
  • random cluster model
  • Markov chain
  • mixing time
  • Swendsen-Wang dynamics
  • holographic transformation


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