Zeros of ferromagnetic 2-spin systems

Understand

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.