A Multi-Body Dobrushin-Sokal Criterion -- Part II
Abstract
We prove a sufficient condition for the absolute convergence of Mayer cluster expansions of log-partition and correlation functions applicable to lattice gases with possibly complex-valued multi-body interactions. Not only are several classical results subsumed but a partition scheme for spanning hypergraphs also makes our methods well-suited for treating stronger multi-body interactions, including higher-order hard-core repulsion in the context of hypergraph independence polynomials. Furthermore, our approach is easily combined with the Gruber--Kunz condition to produce extended convergence results for the polymer expansion of lattice gases, rivalling those obtained not too long ago by Nguyen and Fern\'andez (2024).
Keywords
Cite
@article{arxiv.2606.29404,
title = {A Multi-Body Dobrushin-Sokal Criterion -- Part II},
author = {Jan Philipp Neumann},
journal= {arXiv preprint arXiv:2606.29404},
year = {2026}
}
Comments
27 pages; can be read independently of Part I