分层立方体：吉布斯测量和相关性衰减

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Statistical Physics Pub Date : 2024-11-28 DOI:10.1007/s10955-024-03375-9

Sabine Jansen, Jan Philipp Neumann

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引用次数: 0

摘要

我们研究了一个边长为 \(2^j\), \(j\in {\mathbb {Z}}\) 的非重叠立方体的分层模型。该模型允许任意小的立方体，而且活动不需要平移不变。它也可以被重铸为一个具有长程硬核相互作用的树上自旋系统。我们证明了吉布斯量存在性和唯一性的必要条件和充分条件，讨论了碎片化和凝聚，并证明了两点相关函数的衰减边界。

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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 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.

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来源期刊

Journal of Statistical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

12.50%

发文量

152

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.