Journal of Mathematical Physics, Analysis, Geometry 2019, vol. 15, No 3, pp. 321-335   https://doi.org/10.15407/mag15.03.321     ( to contents , go back )

### On Dynamical Behavior of the p-adic λ-Ising Model on Cayley Tree

Mutlay Dogan

University of Bahamas, Faculty of Pure and Applied Sciences, Oakes Field Campus, N 4912, Nassau, Bahamas
E-mail: mutlay74@gmail.com

Received April 4, 2018, revised June 11, 2018.

Abstract

In the present paper, we continue to study some features of the mixed type $p$-adic $\lambda$-Ising model which was studied in [3]. In that study, the existence of the $p$-adic Gibbs measures and phase transitions were investigated for the model on the Cayley tree of order two. In the current paper, we study the dynamical behavior of the fixed points which have been found in [3]. As the main result, we proved that the fixed point $u_0$ is an attractor and the other fixed points $u_{1,2}$ are repellent fixed points for the mixed type $p$-adic $\lambda$-Ising model. In addition, the size of basin of attractor for the fixed point $u_0$ is described.

Mathematics Subject Classification 2010: 58F12, 46S10, 12J12, 11S99, 54H20, 30D05.
Key words: p-adic numbers, p-adic quasi Gibbs measure, dynamical systems, Cayley tree.