This article is cited in 9 papers

The $p$-adic Potts model on the Cayley tree of order three

F. M. Mukhamedov^a, H. Akin<sup>b

a</sup> Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, Pahang, Malaysia
^b Faculty of Education, Zirve University, Gaziantep, Turkey

Abstract: We study a phase transition problem for the $q$-state $p$-adic Potts model on the Cayley tree of order three. We find certain conditions for the existence of $p$-adic Gibbs measures and then establish the existence of a phase transition.

Keywords: $p$-adic number, Potts model, $p$-adic quasi-Gibbs measure, phase transition.

MSC: 46S10, 82B26, 12J12, 39A70, 47H10, 60K35

Received: 17.02.2013

DOI: 10.4213/tmf8522

 English version: Theoretical and Mathematical Physics, 2013, 176:3, 1267–1279

Bibliographic databases:

• 
• 
• 
• 
• 
• 
•