arXiv subjects

Jan Philipp Neumann

Publications and source records attributed to Jan Philipp Neumann.

3 recordsLinked to original sources

arXiv2026

A Multi-Body Dobrushin-Sokal Criterion -- Part II

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).

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arXiv2025

A Multi-Body Dobrushin-Sokal Criterion -- Part I

We derive a sufficient condition for zero-freeness of partition functions applicable to lattice gases with possibly complex-valued multi-body interactions. This includes the case of hard-core interactions and, in particular, generalises recent results by Galvin et al.\ (2024) and Bencs-Buys (2025) on zero-free polydiscs of hypergraph independence polynomials. We provide two proofs: the first generalises the inductive approach of Bencs and Buys; the second employs the Kirkwood-Salsburg hierarchy. Notably, the central argument of the second proof uses of a certain partition scheme for coverings and, as a by-product, we obtain a direct improvement of Gallavotti and Miracle-Sol\'e's (1968) bounds for the Kirkwood-Salsburg operator.

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arXiv2024

Hierarchical Cubes: Gibbs Measures and Decay of Correlations

We study a hierarchical model of non-overlapping cubes of sidelengths $2^j$, $j \in \mathbb{Z}$. The model allows for cubes of arbitrarily small size and the activities need not be translationally invariant. It can also be recast as a spin system on a tree with long-range hard-core interaction. We prove necessary and sufficient conditions for the existence and uniqueness of Gibbs measures, discuss fragmentation and condensation, and prove bounds on the decay of two-point correlation functions.

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