Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree
We consider the p-adic Ising–Vannimenus model on the Cayley tree of order k = 2. This model contains nearest-neighbor and next-nearest-neighbor interactions. We investigate the model using a new approach based on measure theory (in the p-adic sense) and describe all translation-invariant p-adic quas...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English English English |
| Published: |
Maik Nauka Publishing / Springer SBM
2016
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/58349/ http://irep.iium.edu.my/58349/ http://irep.iium.edu.my/58349/ http://irep.iium.edu.my/58349/1/58349_Translation-invariant%20p-adic%20quasi.pdf http://irep.iium.edu.my/58349/2/58349_Translation-invariant%20p-adic%20quasi_SCOPUS.pdf http://irep.iium.edu.my/58349/3/58349_Translation-invariant%20p-adic%20quasi_WOS.pdf |
| Summary: | We consider the p-adic Ising–Vannimenus model on the Cayley tree of order k = 2. This model contains nearest-neighbor and next-nearest-neighbor interactions. We investigate the model using a new approach based on measure theory (in the p-adic sense) and describe all translation-invariant p-adic quasi-Gibbs measures associated with the model. As a consequence, we can prove that a phase transition exists in the model. Here, “phase transition” means that there exist at least two nontrivial p-adic quasi-Gibbs measures such that one is bounded and the other is unbounded. The methods used are inapplicable in the real case. © 2016, Pleiades Publishing, Ltd. |
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