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Analyticity for Classical Gasses via Recursion

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Abstract

We give a new criterion for a classical gas with a repulsive pair potential to exhibit uniqueness of the infinite volume Gibbs measure and analyticity of the pressure. Our improvement on the bound for analyticity is by a factor \(e^2\) over the classical cluster expansion approach and a factor e over the known limit of cluster expansion convergence. The criterion is based on a contractive property of a recursive computation of the density of a point process. The key ingredients in our proofs include an integral identity for the density of a Gibbs point process and an adaptation of the algorithmic correlation decay method from theoretical computer science. We also deduce from our results an improved bound for analyticity of the pressure as a function of the density.

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Acknowledgements

We thank Tyler Helmuth, Sabine Jansen, Steffen Betsch, Günter Last, and the anonymous referees for many helpful comments on the paper. MM supported in part by NSF grant DMS-2137623. WP supported in part by NSF grants DMS-1847451 and CCF-1934915.

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  1. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, USA

    Marcus Michelen

  2. School of Computer Science, Georgia Institute of Technology, Atlanta, USA

    Will Perkins

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  1. Marcus Michelen
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Correspondence to Will Perkins.

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Michelen, M., Perkins, W. Analyticity for Classical Gasses via Recursion. Commun. Math. Phys. 399, 367–388 (2023). https://doi.org/10.1007/s00220-022-04559-8

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