# A Near-Linear Time Sampler for the Ising Model with External Field

arXiv: https://arxiv.org/abs/2207.09391 · HTML: https://mlsanity.com/paper/2207.09391/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2022.

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

- [Optimizing Solution-Samplers for Combinatorial Problems: The Landscape of Policy-Gradient Methods](https://mlsanity.com/paper/2310.05309/) (2023)
- [Rapid mixing in positively weighted restricted Boltzmann machines](https://mlsanity.com/paper/2604.00963/) (2026)

## Abstract (arXiv)

We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising models with edge activities boldsymbolβ > 1 and external fields boldsymbolλ<1 (or symmetrically, boldsymbolλ>1) on general graphs with bounded or unbounded maximum degree. Our algorithm is based on the field dynamics given in [CFYZ21]. We prove the correctness and efficiency of our algorithm by establishing spectral independence of distribution of the random cluster model and the rapid mixing of Glauber dynamics on the random cluster model in a low-temperature regime, which may be of independent interest.