# Zeros of ferromagnetic 2-spin systems

arXiv: https://arxiv.org/abs/1907.06156 · HTML: https://mlsanity.com/paper/1907.06156/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [Rapid mixing in positively weighted restricted Boltzmann machines](https://mlsanity.com/paper/2604.00963/) (2026)

## Abstract (arXiv)

We study zeros of the partition functions of ferromagnetic 2-state spin systems in terms of the external field, and obtain new zero-free regions of these systems via a refinement of Asano's and Ruelle's contraction method. The strength of our results is that they do not depend on the maximum degree of the underlying graph. Via Barvinok's method, we also obtain new efficient and deterministic approximate counting algorithms. In certain regimes, our algorithm outperforms all other methods such as Markov chain Monte Carlo and correlation decay.