Renormalization Method in p-Adic λ-Model on the Cayley Tree

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• 作者：Farrukh Mukhamedov
• 关键词：p ; adic numbers ; p ; adic quasi Gibbs measure ; Phase transition ; Dynamical system ; Cayley tree
• 刊名：International Journal of Theoretical Physics
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：54
• 期：10
• 页码：3577-3595
• 全文大小：335 KB
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• 作者单位：Farrukh Mukhamedov (1)
  
  1. Department of Computational & Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box, 141, 25710, Kuantan, Pahang, Malaysia
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Quantum Physics
  Elementary Particles and Quantum Field Theory
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9575

文摘

In the present paper, it is proposed the renormalization techniques in the investigation of phase transition phenomena in p-adic statistical mechanics. We mainly study p-adic λ-model on the Cayley tree of order two. We consider generalized p-adic quasi Gibbs measures depending for the λ-model. Such measures are constructed by means of certain recurrence equation, which defines a dynamical system. We study two regimes with respect to parameters. In the first regime we establish that the dynamical system has one attractive and two repelling fixed points, which predicts the existence of a phase transition. In the second regime the system has two attractive and one neutral fixed points, which predicts the existence of a quasi phase transition. A main point of this paper is to verify (i.e. rigorously prove) and confirm that the indicated predictions (via dynamical systems point of view) are indeed true. To establish the main result, we employ the methods of p-adic analysis, and therefore, our results are not valid in the real setting. Keywords p-adic numbers p-adic quasi Gibbs measure Phase transition Dynamical system Cayley tree