Decay of multi-point correlation functions in $\mathbb{Z}^d$

• URL: http://arxiv.org/abs/2208.02416v1
• Date: Thu, 4 Aug 2022 02:53:39 GMT
• Title: Decay of multi-point correlation functions in $\mathbb{Z}^d$
• Authors: Rui Han, Fan Yang
• Abstract summary: We prove multi-point correlation bounds in $mathbbZd$ for arbitrary $dgeq 1$ with symmetrized distances. As applications, we prove multi-point correlation bounds for the Ising model on $mathbbZd$, and multi-point dynamical localization in expectation for uniformly localized disordered systems.
• Score: 7.334752859070876
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove multi-point correlation bounds in $\mathbb{Z}^d$ for arbitrary $d\geq 1$ with symmetrized distances, answering open questions proposed by Sims-Warzel \cite{SW} and Aza-Bru-Siqueira Pedra \cite{ABP}. As applications, we prove multi-point correlation bounds for the Ising model on $\mathbb{Z}^d$, and multi-point dynamical localization in expectation for uniformly localized disordered systems, which provides the first examples of this conjectured phenomenon by Bravyi-K\"onig \cite{BK}.

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