Clustering Bounds on N-Point Correlations for Unbounded Spin Systems

Details Clustering Bounds on N-Point Correlations for Unbounded Spin Systems Clustering Bounds on N-Point Correlations for Unbounded Spin Systems

2009-01-29

arxiv.org/abs/0901.4756v1

Physics

Mathematical Physics

50 pages, Latex

Scientific paper

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.

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