Work

Hierarchical Cubes: Gibbs Measures and Decay of Correlations

Year: 2024

Type: article

Abstract: We study a hierarchical model of non-overlapping cubes of sidelengths $$2^j$$ 2 j , $$j\in {\mathbb {Z}}$$ j ∈ 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 a 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.

Source: Journal of Statistical Physics

DOI: 10.1007/s10955-024-03375-9

Authors: Sabine Jansen, Jan Philipp Neumann

Institutions: Munich Center for Quantum Science and Technology, Ludwig-Maximilians-Universität München

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Deutsche Forschungsgemeinschaft