New class of Gibbs measures for two state Hard-Core model on a Cayley tree

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-06-06 DOI:10.1142/s0219025723500248

R. Khakimov, M. T. Makhammadaliev, F. Haydarov

引用次数: 0

Abstract

In this paper, we consider a Hard-Core $(HC)$ model with two spin values on Cayley trees. The conception of alternative Gibbs measure is introduced and translational invariance conditions for alternative Gibbs measures are found. Also, we show that the existence of alternative Gibbs measures which are not translation-invariant. In addition, we study free energy of the model.

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Cayley树上两态Hard-Core模型的一类新的Gibbs测度

本文考虑Cayley树上具有两个自旋值的Hard-Core $(HC)$模型。引入了备选吉布斯测度的概念，并给出了备选吉布斯测度的平移不变性条件。此外，我们还证明了非平移不变的吉布斯测度的存在性。此外，我们还研究了模型的自由能。

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

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.