On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three

Saburov, Mansoor and Ahmad, Mohd Ali Khameini (2015) On descriptions of all translation invariant p−adic gibbs measures for the potts model on the cayley tree of order three. Mathematical Physics, Analysis and Geometry, 18 (1). pp. 1-33. ISSN 1385-0172

PDF (Article) - Published Version Restricted to Repository staff only Download (574kB) | Request a copy

Abstract

Unlike the real number field, a set of p−adic Gibbs measures of p−adic lattice models of statistical mechanics has a complex structure in a sense that it is strongly tied up with a Diophantine problem over p−adic fields. Recently, all translation-invariant p−adic Gibbs measures of the p−adic Potts model on the Cayley tree of order two were described by means of roots of a certain quadratic equation over some domain of the p−adic field. In this paper, we consider the same problem on the Cayley tree of order three. In this case, we show that all translation-invariant p−adic Gibbs measures of the p−adic Potts model can be described in terms of roots of some cubic equation over Zp \ Z∗p. In own its turn, we also provide a solvability criterion of a general cubic equation over Zp \ Z∗p for p > 3.

Item Type:	Article (Journal)
Additional Information:	6769/49321
Uncontrolled Keywords:	p−adic number, p−adic Potts model, p−adic Gibbs measure
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 Mansoor Saburov
Date Deposited:	01 Feb 2016 11:51
Last Modified:	23 Feb 2016 17:14
URI:	http://irep.iium.edu.my/id/eprint/49321

Actions (login required)

View Item