On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree

Mukhamedov, Farrukh (2013) On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree. Mathematical Physics, Analysis and Geometry, 16 (1). pp. 49-87. ISSN 1385-0172 (P), 1572-9656 (O)

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Abstract

In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider twomode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition.

Item Type:	Article (Journal)
Additional Information:	5537/29716
Uncontrolled Keywords:	p-adic numbers Potts model p-adic quasi Gibbs measure Phase transition
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	23 Apr 2013 15:22
Last Modified:	23 Apr 2013 15:22
URI:	http://irep.iium.edu.my/id/eprint/29716

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