Complexity Classification of the Eight-Vertex Model

Abstract

We prove a complexity dichotomy theorem for the eight-vertex model. For every setting of the parameters of the model, we prove that computing the partition function is either solvable in polynomial time or \#P-hard. The dichotomy criterion is explicit. For tractability, we find some new classes of problems computable in polynomial time. For \#P-hardness, we employ Möbius transformations to prove the success of interpolations.

This submission contains two versions of the same paper, one is the short version and one is the full version