$$H_A$$ -Weakly Periodic $$p$$ -Adic Generalized Gibbs Measures for the $$p$$ -Adic Ising Model on the Cayley Tree of Order Two

IF 0.5 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI:10.1134/s2070046624030038

Muzaffar Rahmatullaev, Zulxumor Abdukaxorova

引用次数: 0

Abstract

In the present paper, we consider a $p$-adic Ising model on a Cayley tree. For this model, $p$-adic analogue of the notion of weakly periodic Gibbs measures is introduced. For some normal subgroup of the group representation of the Cayley tree, the existence of such Gibbs measures is proved. We also study fixed points and their behaviour of the mapping which coincides with weakly periodic quantities of the functional equation. Moreover, the boundedness of such kinds of measures is established, which yields the occurrence of a phase transition.

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二阶 Cayley 树上 $$p$$ -Adic Ising 模型的弱周期 $$H_A$$ -p$$ -Adic 广义吉布斯度量

摘要在本文中，我们考虑了一个 Cayley 树上的 $p$-adic Ising 模型。对于这个模型，我们引入了弱（p）周期吉布斯量（weakly periodic Gibbs measures）的类似概念。对于 Cayley 树的群表示的某些正常子群，证明了这种吉布斯量的存在。我们还研究了与函数方程的弱周期量重合的映射的固定点及其行为。此外，我们还确定了此类度量的有界性，从而得出了相变的发生。

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

P-Adic Numbers Ultrametric Analysis and Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： This is a new international interdisciplinary journal which contains original articles, short communications, and reviews on progress in various areas of pure and applied mathematics related with p-adic, adelic and ultrametric methods, including: mathematical physics, quantum theory, string theory, cosmology, nanoscience, life sciences; mathematical analysis, number theory, algebraic geometry, non-Archimedean and non-commutative geometry, theory of finite fields and rings, representation theory, functional analysis and graph theory; classical and quantum information, computer science, cryptography, image analysis, cognitive models, neural networks and bioinformatics; complex systems, dynamical systems, stochastic processes, hierarchy structures, modeling, control theory, economics and sociology; mesoscopic and nano systems, disordered and chaotic systems, spin glasses, macromolecules, molecular dynamics, biopolymers, genomics and biology; and other related fields.