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Jansen, Sabine and Kolesnikov, Leonid (2022): Cluster Expansions: Necessary and Sufficient Convergence Conditions. In: Journal of Statistical Physics, Vol. 189, No. 3 [PDF, 721kB]


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 Kotecky-Preiss and Fernandez-Procacci are easily recovered. In addition, we deduce new sufficient convergence conditions for hard-core systems in R-d and Z(d) as well as for abstract polymer systems. The latter improves on the Fernandez-Procacci criterion.

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