Journal of Statistical Physics

, Volume 157, Issue 6, pp 1225–1254

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

Article

## 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

## Notes

### Acknowledgments

I am grateful to Roberto Fernández for the time he took to explain me his work and encourage my attempts at extending it. The visits at the University of Utrecht have been supported by the RGLIS short visit Grants 4076 and 4446 from the European Science Foundation (ESF). This work has been also supported by the Austrian Science Fund (FWF), Project W1230-N13. I also want to thank Maria Eichlseder for help with the graphics. I am thankful of the comments of my referees, pushing me towards an improved exposition of the motivation and high-level overviews.

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