The Complexity of Ferromagnetic Two-spin Systems with External Fields

Jingcheng Liu, Pinyan Lu, Chihao Zhang, Marc Herbstritt
2014 International Workshop on Approximation Algorithms for Combinatorial Optimization  
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 #BIShard for Ising model if we allow inconsistent external fields on different nodes. In contrast to these two results, we prove that
more » ... 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.
doi:10.4230/lipics.approx-random.2014.843 dblp:conf/approx/LiuLZ14 fatcat:fwitvao7izfere56ytuag3qrli