Translation-invariant p-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree
Farrukh MukhamedovDepartment of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, Pahang, MalaysiaMansoor SaburovDepartment of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, Pahang, MalaysiaOtabek KhakimovInstitute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan
ABI
Аннотация
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.
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