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

arXiv: https://arxiv.org/abs/2205.01985 · HTML: https://mlsanity.com/paper/2205.01985/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2022.

## Built on by (most cited first, 2 of 2)

- [Approximating the total variation distance between spin systems](https://mlsanity.com/paper/2502.05437/) (2025)
- [Rapid mixing in positively weighted restricted Boltzmann machines](https://mlsanity.com/paper/2604.00963/) (2026)

## Abstract (arXiv)

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.