Cayley树上齐次外场Ising模型的平移不变p进广义Gibbs测度

IF 1.1 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-07-30 DOI:10.1007/s11040-025-09516-0

Zulxumor Abdukaxorova

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引用次数: 0

摘要

本文研究了三阶Cayley树上具有齐次外场的p进Ising模型的平移不变p进广义Gibbs测度，假设为\(p > 3\)。证明了如果\(p \equiv 1 (\operatorname {mod} {6})\)，则存在四个平移不变p进广义Gibbs测度；如果\(p \not \equiv 1 (\operatorname {mod} {6})\)，就有两个。此外，对于任意质数\(p > 3\)，我们在该模型中建立了相变的发生。

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Translation-invariant p-adic generalized Gibbs measures for the Ising model with a homogeneous external field on a Cayley tree

This paper investigates translation-invariant p-adic generalized Gibbs measures for the p-adic Ising model with a homogeneous external field on a Cayley tree of order three, assuming \(p > 3\). We demonstrate that if \(p \equiv 1 (\operatorname {mod} {6})\), then there exist four translation-invariant p-adic generalized Gibbs measures; if \(p \not \equiv 1 (\operatorname {mod} {6})\), there exist exactly two. Additionally, for any prime \(p > 3\), we establish the occurrence of a phase transition in this model.

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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.