The Complexity of Ferromagnetic Two-spin Systems with External Fields

Jingcheng Liu; Pinyan Lu; Chihao Zhang

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arXiv · 1402.4346

The Complexity of Ferromagnetic Two-spin Systems with External Fields

Jingcheng Liu·Pinyan Lu·Chihao Zhang

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Abstract

We study the approximability of computing the partition function for ferromagnetic two-state spin systems. The remarkable algorithm by Jerrum and Sinclair showed that there is a fully polynomial-time randomized approximation scheme (FPRAS) for the special ferromagnetic Ising model with any given uniform external field. Later, Goldberg and Jerrum proved that it is #BIS-hard for Ising model if we allow inconsistent external fields on different nodes. In contrast to these two results, we prove that for any ferromagnetic two-state spin systems except the Ising model, there exists a threshold for external fields beyond which the problem is #BIS-hard, even if the external field is uniform.

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Jingcheng Liu, Pinyan Lu, Chihao Zhang. 2014-02-18. The Complexity of Ferromagnetic Two-spin Systems with External Fields. https://arxiv.org/abs/1402.4346

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