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

• Authors: M. Dogan , H. Akin , F. Mukhamedov
• Languages of publication: EN

Abstracts

EN

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 Q_{p}, where p is a prime number p ≥ 3. One of the roots is in ε_{p} and the others are in Q_{p}\ε_{p}. 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.

Keywords

EN

05.50.+q; 02.20.Qs

Discipline

• 05.50.+q: Lattice theory and statistics (Ising, Potts, etc.)(see also 64.60.Cn Order-disorder transformations, and 75.10.Hk Classical spin models)
• 02.20.Qs: General properties, structure, and representation of Lie groups

• Journal: Acta Physica Polonica A
• Year: 2016
• Volume: 129
• Issue: 4
• Pages: 861-864

Dates

published

2016-04

Contributors

author

M. Dogan

• Department of Computational and Theoretical Sciences, Faculty of Science, IIUM, 25200 Kuantan, Malaysia

author

H. Akin

• Zirve University, Faculty of Education, Department of Mathematics, Gaziantep, 27260, Turkey

author

F. Mukhamedov

• Department of Computational and Theoretical Sciences, Faculty of Science, IIUM, 25200 Kuantan, Malaysia

References

• [1] M. Khamraev, F. Mukhamedov, J. Math. Phys. 45, 4025 (2004), doi: 10.1063/1.1792932
• [2] A. Khrennikov, S. Ludkovsky, Adv. Stud. Contemp. Math. 5, 57 (2002)
• [3] F. Mukhamedov, M. Dogan, Rep. Math. Phys. 75, 25 (2015), doi: 10.1016/S0034-4877(15)60022-2
• [4] F. Mukhamedov, H. Akın, J. Math. Anal. Appl. 423, 1203 (2015), doi: 10.1016/j.jmaa.2014.10.046
• [5] F. Mukhamedov, M. Dogan, H. Akın, J. Stat. Mech. Theory Exp. 2014, P10031 (2014), doi: 10.1088/1742-5468/2014/10/P10031

Identifiers

DOI

10.12693/APhysPolA.129.861