The Complexity of Ferromagnetic Two-spin Systems with External Fields
Computational Complexity
2014-02-19 v1 Data Structures and Algorithms
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.
Cite
@article{arxiv.1402.4346,
title = {The Complexity of Ferromagnetic Two-spin Systems with External Fields},
author = {Jingcheng Liu and Pinyan Lu and Chihao Zhang},
journal= {arXiv preprint arXiv:1402.4346},
year = {2014}
}