Some Non-periodic p-Adic Generalized Gibbs Measures for the Ising Model on a Cayley Tree of Order k

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2023-08-31 DOI:10.1007/s11040-023-09465-6

Muzaffar Rahmatullaev, Akbarkhuja Tukhtabaev

引用次数: 0

Abstract

In the present paper, we consider a p-adic Ising model on a Cayley tree. The existence of non-periodic p-adic generalized Gibbs measures of this model is investigated. In particular, we construct p-adic analogue of the Bleher–Ganikhodjaev construction and generalize some constructive methods. Moreover, the boundedness of obtained measures are established, which yields the occurrence of a phase transition.

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k阶Cayley树上Ising模型的一些非周期p进广义Gibbs测度

本文考虑Cayley树上的p进Ising模型。研究了该模型的非周期p进广义Gibbs测度的存在性。特别地，我们构造了Bleher-Ganikhodjaev构造的p进类似，并推广了一些构造方法。此外，建立了所得测度的有界性，从而得出相变的发生。

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

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.