# Random cluster dynamics for the Ising model is rapidly mixing

arXiv: https://arxiv.org/abs/1605.00139 · HTML: https://mlsanity.com/paper/1605.00139/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2016.

## Built on by (most cited first, 3 of 3)

- [Glauber Generative Model: Discrete Diffusion Models via Binary Classification](https://mlsanity.com/paper/2405.17035/) (2024)
- [Sampling Approximately Low-Rank Ising Models: MCMC meets Variational Methods](https://mlsanity.com/paper/2202.08907/) (2022)
- [Rapid mixing in positively weighted restricted Boltzmann machines](https://mlsanity.com/paper/2604.00963/) (2026)

## Abstract (arXiv)

We show that the mixing time of Glauber (single edge update) dynamics for the random cluster model at q=2 is bounded by a polynomial in the size of the underlying graph. As a consequence, the Swendsen-Wang algorithm for the ferromagnetic Ising model at any temperature has the same polynomial mixing time bound.