Single Scale Cluster Expansions with Applications to Many Boson and\n Unbounded Spin Systems

2014/11/04 by Martin Lohmann, Lohmann, Martin
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Complex Systems and Time Series Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1411.1107

openalex publication_date 2014/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a cluster expansion to show exponential decay of correlations for\nquite general single scale spin systems, as they arise in lattice quantum field\ntheory and discretized functional integral representations for observables of\nquantum statistical mechanics. We apply our results to: the small field\napproximation to the coherent state correlation functions of the grand\ncanonical Bose gas at negative chemical potential, constructed by Balaban,\nFeldman, Kn "orrer and Trubowitz (2010); and to N component unbounded spin\nsystems with repulsive two body interaction and massive, possibly complex,\ncovariance. Our cluster expansion is derived by a single application of the\nBKAR interpolation formula.\n

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