Existence of phase transition for 1d-countable state P -adic Potts model

Mukhamedov, Farrukh (2012) Existence of phase transition for 1d-countable state P -adic Potts model. In: Proceedings of Turin Polytechnic University in Tashkent. ASR MATBUOT” ltd., Tashkent, Uzbekistan, pp. 228-242.

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Abstract

In the present paper we shall consider countable state p -adic Potts model on Z . A main aim is to establish the existence of the phase transition for the model. In our study, we essentially use one dimensionality of the model. The existence of the phase transition is reduced to the investigation of an infinitedimensional nonlinear equation. We find a condition on weights to show that the derived equation has two solutions, which yields the existence of the phase transition. We prove that measures corresponding to first and second solutions are a p -adic Gibbs and generalized p -adic Gibbs measures, respectively. Note that it turns out that the finding condition does not depend on values of the prime p , and therefore, an analogous fact is not true when the number of spins is finite

Item Type:	Book Chapter
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:	31 Dec 2012 11:40
Last Modified:	31 Dec 2012 11:40
URI:	http://irep.iium.edu.my/id/eprint/26068

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