A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two

Mukhamedov, Farrukh (2012) A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two. Reports on Mathematical Physics, 70 (3). pp. 385-406. ISSN 00344877

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Abstract

In the present paper, we introduce a new kind of p-adic measures for (q + 1)-state Potts model, called generalized p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. We employ a dynamical system approach to establish phase transition phenomena for the given model. Namely, using the derived recursive relations we define a one-dimensional fractional p-adic dynamical system. We show that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. In this case, there exists a strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields the existence of a quasi phase transition.

Item Type:	Article (Journal)
Additional Information:	5537/28682
Uncontrolled Keywords:	p-adic numbers, Potts model; p-adic quasi Gibbs measure, phase transition
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
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:	22 Jan 2013 14:48
Last Modified:	13 Feb 2013 17:42
URI:	http://irep.iium.edu.my/id/eprint/28682

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