A New Correlation Inequality for Ising models with external fields

29.11.2021 16:15 – 18:15

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 maximised when the external field is identically $0$. One corollary is that spin-spin correlations are maximised when the external field vanishes and the boundary condition is free, which proves a conjecture of Shlosman. In particular, the random field Ising model on $\Z^d$, $d\geq 3$, 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 $d\geq 3$ satisfies the conjectured strong spatial mixing property in the entire high temperature regime. This is a joint work with Jian Ding and Rongfeng Sun.

Lieu

Conseil Général 7-9, Salle 1-15, Séminaire "Mathématique physique"

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