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On p-adic Gibbs measures of the countable state Potts model on the Cayley tree.
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Matematik.ORCID iD: 0000-0002-9857-0938
2007 (English)In: Nonlinearity, ISSN 0951-7715, Vol. 20, no 12, p. 2923-2937Article in journal (Refereed) Published
Abstract [en]

In this paper we consider the countable state p-adic Potts model on the Cayley tree. A construction of p-adic Gibbs measures which depends on weights λ is given, and an investigation of such measures is reduced to the examination of an infinite-dimensional recursion equation. By studying the derived equation under some condition concerning weights, we prove the absence of a phase transition. Note that the condition does not depend on values of the prime p, and the analogous fact is not true when the number of spins is finite. For the homogeneous model it is shown that the recursive equation has only one solution under that condition on weights. This means that there is only one p-adic Gibbs measure μλ. The boundedness of the measure is also established. Moreover, the continuous dependence of the measure μλ on λ is proved. At the end we formulate a one limit theorem for μλ.

Place, publisher, year, edition, pages
IOP Publ. Ltd , 2007. Vol. 20, no 12, p. 2923-2937
Keyword [en]
p-adic Gibbs measures
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:vxu:diva-2934DOI: doi:10.1088/0951-7715/20/12/010OAI: oai:DiVA.org:vxu-2934DiVA, id: diva2:202890
Available from: 2007-12-25 Created: 2007-12-25 Last updated: 2016-05-03Bibliographically approved

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Publisher's full texthttp://www.iop.org/EJ/abstract/0951-7715/20/12/010/

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Khrennikov, Andrei

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Citation style
  • apa
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  • vancouver
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • text
  • asciidoc
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