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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 thatdoi:10.4230/lipics.approx-random.2014.843 dblp:conf/approx/LiuLZ14 fatcat:fwitvao7izfere56ytuag3qrli