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International Conference on Stochastic Processes and Algebraic Structures

SPAS 2017: Algebraic Structures and Applications pp 935–944Cite as

Uniqueness of p-Adic Gibbs Measures for p-Adic \(\lambda \)-Ising Model on Cayley Tree of Arbitrary Order

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 317))

Abstract

In this chapter, we consider an interaction of the nearest-neighbors and next nearest-neighbors for the mixed type p-adic \(\lambda \)-Ising model with spin values \(\left\{ -1,+1\right\} \) on Cayley tree of arbitrary order. We prove the existence and uniqueness of the p-adic Gibbs measures for the mixed type p-adic \(\lambda \)-Ising model on the Cayley tree of arbitrary order.

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Acknowledgements

The author thanks to Prof. Dr. Farrukh Mukhamedov and Prof. Dr. Hasan Akin for their valuable ideas and supports.

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Authors and Affiliations

  1. Faculty of Pure and Applied Sciences, School of Mathematics, Physics and Technology, University of Bahamas, Nassau, Bahamas

    Mutlay Dogan

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  1. Mutlay Dogan
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Correspondence to Mutlay Dogan .

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Editors and Affiliations

  1. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

  2. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Anatoliy Malyarenko

  3. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Milica Rančić

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Dogan, M. (2020). Uniqueness of p-Adic Gibbs Measures for p-Adic \(\lambda \)-Ising Model on Cayley Tree of Arbitrary Order. In: Silvestrov, S., Malyarenko, A., Rančić, M. (eds) Algebraic Structures and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-030-41850-2_39

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