Approximating Partition Functions of Two-State Spin Systems

TL;DR

This paper develops an efficient approximation scheme for the partition function of two-state spin systems on bounded degree graphs, leveraging correlation decay properties under certain temperature conditions, with sharp results for the Ising model.

Contribution

It introduces an FPTAS for the partition function based on correlation decay, applicable under conditions proven to be sharp for the Ising model.

Findings

Proves strong correlation decay for small inverse temperature.

Develops an FPTAS for the partition function.

Establishes sharpness of conditions for the Ising model.

Abstract

Two-state spin systems is a classical topic in statistical physics. We consider the problem of computing the partition function of the systems on a bounded degree graph. Based on the self-avoiding tree, we prove the systems exhibits strong correlation decay under the condition that the absolute value of "inverse temperature" is small. Due to strong correlation decay property, an FPTAS for the partition function is presented under the same condition. This condition is sharp for Ising model.