Abstract We study a hierarchical model of non-overlapping cubes of sidelengths $$2^j$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>j</mml:mi> </mml:msup> </mml:math> , $$j\in {\mathbb {Z}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>j</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>Z</mml:mi> </mml:mrow> </mml:math> . 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.

Sabine Jansen

Jan Philipp Neumann

Journal of Statistical Physics

《统计物理学杂志》在统计物理学的所有领域以及与物理系统中的集体现象有关的相关领域发表原创和特邀评论论文。

The Journal of Statistical Physics publishes original research articles and invited reviews in all areas of statistical physics, with a particular emphasis on topics related to collective phenomena in physical systems.

《Journal of Statistical Physics》致力于发表统计物理学各个领域的原创研究论文和特邀评论，特别关注与物理系统中的集体现象相关的研究。

Category	Quartile
物理与天体物理	3
物理与天体物理, 物理数学物理	3

Hierarchical Cubes: Gibbs Measures and Decay of Correlations

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Journal Info

Category	Quartile
PHYSICS, MATHEMATICAL	3