Clustering Bounds on N-Point Correlations for Unbounded Spin Systems

TL;DR

This paper establishes clustering bounds for unbounded spin systems' correlations across various regimes, using cluster expansion techniques, aiding the understanding of quantum fluids at low temperatures.

Contribution

It provides a unified approach to clustering estimates in different regimes of unbounded spin systems, including the low temperature case relevant for quantum fluids.

Findings

Clustering estimates proven for multiple regimes.

Unified treatment via cluster expansion techniques.

Results applicable to quantum fluid kinetic scale analysis.

Abstract

We prove clustering estimates for the truncated correlations, i.e., cumulants of an unbounded spin system on the lattice. We provide a unified treatment, based on cluster expansion techniques, of four different regimes: large mass, small interaction between sites, large self-interaction, as well as the more delicate small self-interaction or `low temperature' regime. A clustering estimate in the latter regime is needed for the Bosonic case of the recent result obtained by Lukkarinen and Spohn on the rigorous control on kinetic scales of quantum fluids.