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arXiv · 2406.06249

Hierarchical Cubes: Gibbs Measures and Decay of Correlations

Sabine Jansen·Jan Philipp Neumann
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Abstract

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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Sabine Jansen, Jan Philipp Neumann. 2024-06-10. Hierarchical Cubes: Gibbs Measures and Decay of Correlations. https://doi.org/10.1007/s10955-024-03375-9

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