Clustering Bounds on N-Point Correlations for Unbounded Spin Systems

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.

50 pages, Latex

References in corpus (5)

• Weakly nonlinear Schrödinger equation with random initial data
• Cluster expansion for abstract polymer models. New bounds from an old approach
• Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids
• Clustering of fermionic truncated expectation values via functional integration
• On the Exponential Decay of the n-point Correlation Functions and the Analyticity of the Pressure

Cited by in corpus (5)

• Weakly nonlinear Schrödinger equation with random initial data
• Asymptotic quantum many-body localization from thermal disorder
• Wick polynomials and time-evolution of cumulants
• Summability of joint cumulants of nonindependent lattice fields
• Asymptotic linearity of binomial random hypergraphs via cluster expansion under graph-dependence