On the strong phase transition for the one-dimensional countable statep-adic Potts model

Mukhamedov, Farrukh (2014) On the strong phase transition for the one-dimensional countable statep-adic Potts model. Journal of Statistical Mechanics: Theory and Experiment, 2014 (P01007). pp. 1-23. ISSN 1742-5468 (O)

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Abstract

In the present paper we consider the countable state p-adic Potts model on Z+. A main aim is to establish the existence of the strong phase transition for the model. In our study, we essentially use one dimensionality of the model. To prove the existence of the phase transition, we reduce the problem to the investigation of an in�nite-dimensional nonlinear equation. We �nd a condition on weights to show that the derived equation has two solutions. We show that measures corresponding to �rst and second solutions are a p-adic Gibbs and generalized p-adic Gibbs measures, respectively. Moreover, it is proved that the p-adic Gibbs measure is bounded, and the generalized one is not bounded. This implies the existence of the strong phase transition. Note that it turns out that the obtained condition does not depend on values of the prime p and, therefore, an analogous fact is not true when the number of spins is �nite. Note that, in the usual real case, if one considers a one-dimensional translation- invariant model with nearest neighbor interaction, then such a model does not exhibit a phase transition. Nevertheless, we should stress that our model exhibits a unique p-adic Gibbs measure.

Item Type:	Article (Journal)
Additional Information:	5537/35681
Uncontrolled Keywords:	rigorous results in statistical mechanics, solvable lattice models, phase diagrams (theory), renormalization group
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:	19 Feb 2014 11:12
Last Modified:	19 Feb 2014 11:12
URI:	http://irep.iium.edu.my/id/eprint/35681

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