Abstract
In the present paper, we consider the p-adic λ-model on the Cayley tree of order two. It is considered generalized p-adic quasi Gibbs measure depending on a parameter ρ ∈ p, for the λ-model. In the p-adic setting there are several kinds of phase transitions such as storing phase transition, phase transition in terms of the generalized p-adic quasi Gibbs measures. In the paper, we consider two regimes with respect to the parameter ρ. The existence of generalized p-adic Gibbs measures in both regimes is proved. We prove the existence of the phase transition for the p-adic λ model on the Cayley tree of order two in the first regime. It turns out that in the second regime, we are able to establish the strong phase transition for a class of λ-models on the same tree. To prove the main results, we employ the methods of p-adic analysis, and therefore, our results are not valid in the real setting.
Original language | English |
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Pages (from-to) | 25-46 |
Number of pages | 22 |
Journal | Reports on Mathematical Physics |
Volume | 75 |
Issue number | 1 |
DOIs | |
Publication status | Published - Feb 1 2015 |
Externally published | Yes |
Keywords
- Cayley tree
- P-adic numbers
- P-adic quasi Gibbs measure
- Phase transition
- λ-model
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics