Complexity Classification Of The Six-Vertex Model

TL;DR

This paper establishes a clear complexity classification for the six-vertex model's partition function, showing it is either efficiently computable or computationally hard depending on the parameters.

Contribution

It provides the first explicit complexity dichotomy theorem for the six-vertex model's partition function across all parameter settings.

Findings

Partition function is either polynomial-time computable or #P-hard.

The dichotomy criterion for complexity is explicitly characterized.

The result applies to all parameter configurations of the model.

Abstract

We prove a complexity dichotomy theorem for the six-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.