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

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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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Acknowledgements

The authors gratefully acknowledge the many helpful suggestions of Prof. Utkir A. Rozikov during the preparation of the paper. We also thank the referees for the careful reading of the manuscript and especially for a number of suggestions that have improved the paper.

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  1. Muzaffar Rahmatullaev and Akbarkhuja Tukhtabaev have been contributed equally to this work.

Authors and Affiliations

  1. Institute of Mathematics, Academy of Science, 9, University str, 100174, Tashkent, Uzbekistan

    Muzaffar Rahmatullaev

  2. New Uzbekistan University, 54 Mustaqillik Ave., 100174, Tashkent, Uzbekistan

    Muzaffar Rahmatullaev

  3. Namangan State University, Uychi Street, 160136, Namangan, Uzbekistan

    Akbarkhuja Tukhtabaev

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  1. Muzaffar Rahmatullaev
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  2. Akbarkhuja Tukhtabaev
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Correspondence to Akbarkhuja Tukhtabaev.

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Rahmatullaev, M., Tukhtabaev, A. Some Non-periodic p-Adic Generalized Gibbs Measures for the Ising Model on a Cayley Tree of Order k. Math Phys Anal Geom 26, 22 (2023). https://doi.org/10.1007/s11040-023-09465-6

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