Speaker: Shuai Shao, Distinguished Professor, School of Computer Science and Technology, University of Science and Technology of China

Date: April 1, 2024

Time: 14:00-16:00

Location: Conference Room 310, Office Building, School of Software, Shandong University

Sponsor: School of Software, Shandong University

Abstract:

In this talk, we show how to derive the strong spatial mixing property for 2-spin systems from zero-free regions of its partition function. We view the partition function of 2-spin systems as a multivariate function over three complex variables (β,γ,λ), and we allow the zero-free regions of β,γ or λ to be of arbitrary shapes. As long as the zero-free region contains a positive point and it is a complex neighborhood of λ = 0 when fixing β,γ ∈ C , or a complex neighborhood of βγ = 1 when fixing β,λ ∈ C or γ,λ ∈ C, we are able to show that the corresponding 2-spin system exhibits strong spatial mixing on such a region. The underlying graphs of the 2-spin system are not necessarily of bounded degree, while are required to include graphs with pinned vertices. We prove this result by establishing a Christoffel-Darboux type identity for the 2-spin system on trees and using certain tools from complex analysis.

To our best knowledge, our result is general enough to turn all currently known zero-free regions of the partition function of 2-spin systems where pinned vertices are allowed into the strong spatial mixing property. Moreover, we apply our result to obtain strong spatial mixing for the ferromagnetic Ising model from the celebrated Lee-Yang circle theorem.

Based on joint work with Ke Shi and Xiaowei Ye.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/189036.htm