Complexity Classification of the Eight-Vertex Model
Computational Complexity
2017-03-31 v2 Statistical Mechanics
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 M\"{o}bius transformations to prove the success of interpolations.
Cite
@article{arxiv.1702.07938,
title = {Complexity Classification of the Eight-Vertex Model},
author = {Jin-Yi Cai and Zhiguo Fu},
journal= {arXiv preprint arXiv:1702.07938},
year = {2017}
}
Comments
This submission contains two versions of the same paper, one is the short version and one is the full version