Existence of gradient Gibbs measures on regular trees which are not translation invariant

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-02-23 DOI:10.1214/22-aap1883

Florian Henning, C. Kuelske

引用次数: 15

Abstract

We provide an existence theory for gradient Gibbs measures for Z-valued spin models on regular trees which are not invariant under translations of the tree, assuming only summability of the transfer operator. The gradient states we obtain are delocalized. The construction we provide for them starts from a two-layer hidden Markov model representation in a setup which is not invariant under tree-automorphisms, involving internal q-spin models. The proofs of existence and lack of translation invariance of infinite-volume gradient states are based on properties of the local pseudo-unstable manifold of the corresponding discrete dynamical systems of these internal models, around the free state, at large q.

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正则树上非平移不变量的梯度Gibbs测度的存在性

我们提供了正则树上Z值自旋模型的梯度Gibbs测度的存在性理论，该模型在树的平移下不是不变的，只假设转移算子的可和性。我们得到的梯度态是离域的。我们为它们提供的构造从两层隐马尔可夫模型表示开始，该模型在树自同构下是不不变的，涉及内部q-spin模型。无限体积梯度态平移不变性的存在性和缺乏性的证明是基于这些内部模型的相应离散动力系统的局部伪不稳定流形的性质，在自由态周围，大q。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.