Sufficient conditions for uniform bounds in abstract polymer systems and explorative partition schemes. (English) Zbl 1310.82056

Summary: 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 R. L. Dobrushin’s classic condition [Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 177(32), 59–81 (1996; Zbl 0873.60074)]. All conditions arise from an extension of the tree-operator approach introduced by R. Fernández and A. Procacci [Commun. Math. Phys. 274, No. 1, 123–140 (2007; Zbl 1206.82148)] 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.


82D60 Statistical mechanics of polymers
05C05 Trees
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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