Jian Ding - A New Correlation Inequality for Ising Models with External Fields
|Dates:||24 November 2021|
|Times:||15:00 - 16:00|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
Jian Ding (University of Pennsylvania) will speak in the Probability seminar.
We study ferromagnetic Ising models on finite graphs with an inhomogeneous external field, where a subset of vertices is designated as the boundary. We show that the influence of boundary conditions on any given spin is maximized when the external field is identically 0. One corollary is that spin-spin correlations are maximized when the external field vanishes and the boundary condition is free, which proves a conjecture of Shlosman. In particular, the random field Ising model in three dimensions and above exhibits exponential decay of correlations in the entire high temperature regime of the pure Ising model. Another corollary is that the pure Ising model in three dimensions and higher satisfies the conjectured strong spatial mixing property in the entire high temperature regime. Joint work with Jian Song and Rongfeng Sun.
Travel and Contact Information