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

Abstract

We prove multi-point correlation bounds in Z d for arbitrary d ≥ 1 with symmetrized distances, answering open questions proposed by Sims-Warzel [43] and Aza-Bru-Siqueira Pedra [11]. As applications, we prove multi-point correlation bounds for the Ising model on 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-König [14].