Uniqueness, Spatial Mixing, and Approximation for Ferromagnetic 2-Spin Systems

TL;DR

This paper develops FPTAS algorithms for ferromagnetic 2-spin systems' partition functions using a novel potential function to establish spatial mixing, nearly reaching the theoretical threshold.

Contribution

Introduces a new potential function enabling spatial mixing analysis, leading to near-optimal FPTAS for ferromagnetic 2-spin systems.

Findings

FPTAS achieved for certain parameter regimes

Threshold close to the integrality gap

New correlation decay technique based on the potential function

Abstract

We give fully polynomial-time approximation schemes (FPTAS) for the partition function of ferromagnetic 2-spin systems in certain parameter regimes. The threshold we obtain is almost tight up to an integrality gap. Our technique is based on the correlation decay framework. The main technical contribution is a new potential function, with which we establish a new kind of spatial mixing.