The Potts model with countable set of spin values on a Cayley tree

We consider a nearest-neighbor Potts model, with countable spin values 0, 1, . . .,and non zero external field, on a Cayley tree of order k (with k+1 neighbors). We study translation-invariant ‘splitting’ Gibbs measures. We reduce the problem to the description of the solutions of some infinite sys...

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Main Authors:	Ganikhodjaev, Nasir, Rozikov, Utkir Abdulloevich
Format:	Article
Language:	English
Published:	Springer Netherlands 2006
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/14417/ http://irep.iium.edu.my/14417/ http://irep.iium.edu.my/14417/ http://irep.iium.edu.my/14417/1/gnnru_lmp%2806%29%5B1%5D.pdf

id	iium-14417
recordtype	eprints
spelling	iium-144172012-05-31T02:33:27Z http://irep.iium.edu.my/14417/ The Potts model with countable set of spin values on a Cayley tree Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich QA Mathematics We consider a nearest-neighbor Potts model, with countable spin values 0, 1, . . .,and non zero external field, on a Cayley tree of order k (with k+1 neighbors). We study translation-invariant ‘splitting’ Gibbs measures. We reduce the problem to the description of the solutions of some infinite system of equations. For any k�1 and any fixed probability measure ν with ν(i)>0 on the set of all non negative integer numbers Φ={0, 1, . . . } we show that the set of translation-invariant splitting Gibbs measures contains at most one point, independently on parameters of the Potts model with countable set of spin values on Cayley tree. Also we give description of the class of measures ν on Φ such that with respect to each element of this class our infinite system of equations has unique solution {ai , i =1, 2, . . . }, where a ∈(0, 1). Springer Netherlands 2006 Article PeerReviewed application/pdf en http://irep.iium.edu.my/14417/1/gnnru_lmp%2806%29%5B1%5D.pdf Ganikhodjaev, Nasir and Rozikov, Utkir Abdulloevich (2006) The Potts model with countable set of spin values on a Cayley tree. Letters in Mathematical Physics, 75 (2). pp. 99-109. ISSN 0377-9017 (P), 1573-0530 (O) http://www.springerlink.com/content/yp736185774p5304/ 10.1007/s11005-005-0032-8
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich The Potts model with countable set of spin values on a Cayley tree
description	We consider a nearest-neighbor Potts model, with countable spin values 0, 1, . . .,and non zero external field, on a Cayley tree of order k (with k+1 neighbors). We study translation-invariant ‘splitting’ Gibbs measures. We reduce the problem to the description of the solutions of some infinite system of equations. For any k�1 and any fixed probability measure ν with ν(i)>0 on the set of all non negative integer numbers Φ={0, 1, . . . } we show that the set of translation-invariant splitting Gibbs measures contains at most one point, independently on parameters of the Potts model with countable set of spin values on Cayley tree. Also we give description of the class of measures ν on Φ such that with respect to each element of this class our infinite system of equations has unique solution {ai , i =1, 2, . . . }, where a ∈(0, 1).
format	Article
author	Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich
author_facet	Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich
author_sort	Ganikhodjaev, Nasir
title	The Potts model with countable set of spin values on a Cayley tree
title_short	The Potts model with countable set of spin values on a Cayley tree
title_full	The Potts model with countable set of spin values on a Cayley tree
title_fullStr	The Potts model with countable set of spin values on a Cayley tree
title_full_unstemmed	The Potts model with countable set of spin values on a Cayley tree
title_sort	potts model with countable set of spin values on a cayley tree
publisher	Springer Netherlands
publishDate	2006
url	http://irep.iium.edu.my/14417/ http://irep.iium.edu.my/14417/ http://irep.iium.edu.my/14417/ http://irep.iium.edu.my/14417/1/gnnru_lmp%2806%29%5B1%5D.pdf
first_indexed	2023-09-18T20:23:36Z
last_indexed	2023-09-18T20:23:36Z
_version_	1777408269377077248

The Potts model with countable set of spin values on a Cayley tree

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