Cluster Expansions: Necessary and Sufficient Convergence Conditions

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

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 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0022-4715
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892