Journal of Statistical Physics

, Volume 157, Issue 6, pp 1225–1254 | Cite as

Sufficient Conditions for Uniform Bounds in Abstract Polymer Systems and Explorative Partition Schemes

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Abstract

We present several new sufficient conditions for uniform boundedness of the reduced correlations and free energy of an abstract polymer system in a complex multidisc around zero fugacity. They resolve a discrepancy between two incomparable and previously known extensions of Dobrushin’s classic condition. All conditions arise from an extension of the tree-operator approach introduced by Fernández and Procacci combined with a novel family of partition schemes of the spanning subgraph complex of a cluster. The key technique is the increased transfer of structural information from the partition scheme to a tree-operator on an enhanced space.

Keywords

Cluster expansion Abstract polymer system Partition scheme Tree-operator Hardcore gas 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesVU University AmsterdamAmsterdamThe Netherlands

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