Existence of p-Adic Quasi Gibbs Measures for Mixed Type p-Adic Ising λ-Model

M. Dogana, H. Akina and F. Mukhamedovb aZirve University, Faculty of Education, Department of Mathematics, Gaziantep, 27260, Turkey bDepartment of Computational and Theoretical Sciences, Faculty of Science, IIUM, 25200 Kuantan, Malaysia

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We consider nearest-neighbors and next nearest-neighbors p-adic Ising λ-model with spin values {∓ 1} on a Cayley tree of order two. First we prove that the model satisfies the Kolmogorov consistency condition and then we prove that the nonlinear equation corresponding to the model has at least two solutions in Qp, where p is a prime number p ≥ 3. One of the roots is in εp and the others are in Qp\εp. If the nonlinear equation has more than one non-trivial solutions for the model then we conclude that p-adic quasi Gibbs measure exists for the model.

DOI: 10.12693/APhysPolA.129.861 PACS numbers: 05.50.+q, 02.20.Qs