TY - JOUR
T1 - On P-Adic λ-model on the cayley tree II
T2 - Phase transitions
AU - Mukhamedov, Farrukh
AU - Dogan, Mutlay
N1 - Funding Information:
The first author (F.M.) thanks the MOE grant ERGS13-024-0057 and the Junior Associate scheme of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. This work is a part of the second author's PhD thesis.
Publisher Copyright:
© 2015 Polish Scientific Publishers.
PY - 2015/2/1
Y1 - 2015/2/1
N2 - 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.
AB - 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.
KW - Cayley tree
KW - P-adic numbers
KW - P-adic quasi Gibbs measure
KW - Phase transition
KW - λ-model
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U2 - 10.1016/S0034-4877(15)60022-2
DO - 10.1016/S0034-4877(15)60022-2
M3 - Article
AN - SCOPUS:84922702183
SN - 0034-4877
VL - 75
SP - 25
EP - 46
JO - Reports on Mathematical Physics
JF - Reports on Mathematical Physics
IS - 1
ER -