Speaker:

Yin Yitong

Title:

Correlation Decay up to Uniqueness in Spin Systems

Abstract:

We give a complete characterization of the two-state anti-ferromagnetic spin systems which are of exponential correlation decay. We show that a system is of correlation decay on all graphs with maximum degree \Delta\ if and only if the system has a unique Gibbs measure on all infinite regular trees up to degree \Delta, where \Delta\ can either be bounded or unbounded. As a consequence, an FPTAS exists for computing the partition function of a spin system when the parameters of the system satisfy the uniqueness condition. The uniqueness of Gibbs measure on regular trees is a fundamental property for spin systems, which has a closed form formulation in terms of the parameters specifying the system, and is believed to characterize the approximability of the partition function of a two-state anti-ferromagnetic spin system.

This talk is based on a joint work with Liang Li and Pinyan Lu.