Cluster Expansions: Necessary and Sufficient Convergence Conditions

Jansen, Sabine und Kolesnikov, Leonid (2022): Cluster Expansions: Necessary and Sufficient Convergence Conditions. In: Journal of Statistical Physics, Bd. 189, Nr. 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0022-4715
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892