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arXiv · 2112.13134

Cluster expansions: Necessary and sufficient convergence conditions

Sabine Jansen·Leonid Kolesnikov
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Abstract

We prove a new convergence condition for the activity expansion of correlation functions in equilibrium statistical mechanics with possibly negative pair potentials. For non-negative pair potentials, the criterion is an if and only if condition. The condition is formulated with a sign-flipped Kirkwood-Salsburg operator and known conditions such as Koteck${\'y}$-Preiss and Fern${\'a}$ndez-Procacci are easily recovered. In addition, we deduce new sufficient convergence conditions for hard-core systems in $\mathbb R^d$ and $\mathbb Z^d$ as well as for abstract polymer systems. The latter improves on the Fern${\'a}$ndez-Procacci criterion.

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Sabine Jansen, Leonid Kolesnikov. 2021-12-24. Cluster expansions: Necessary and sufficient convergence conditions. https://doi.org/10.1007/s10955-022-02992-6

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