On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree
In this paper, we continue an investigation of the p-adic Ising– Vannimenus model on the Cayley tree of an arbitrary order k (k > 2). We prove the existence of p-adic quasi Gibbs measures by analyzing fixed points of multidimensional p-adic system of equations. We are also able to show the uni...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute of Physics Publishing Ltd.
2015
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/44018/ http://irep.iium.edu.my/44018/ http://irep.iium.edu.my/44018/ http://irep.iium.edu.my/44018/1/mfmsokh-jstat-2015.pdf |
| Summary: | In this paper, we continue an investigation of the p-adic Ising–
Vannimenus model on the Cayley tree of an arbitrary order k (k > 2). We prove
the existence of p-adic quasi Gibbs measures by analyzing fixed points of multidimensional
p-adic system of equations. We are also able to show the uniqueness
of translation-invariant p-adic Gibbs measure. Finally, it is established the
existence of the phase transition for the Ising–Vannimenus model depending on
the order k of the Cayley tree and the prime p. Note that the methods used in
the paper are not valid in the real setting, since all of them are based on p-adic
analysis and p-adic probability measures. |
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