English

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.

Keywords

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

R2 v1 2026-06-22T18:28:28.604Z