On pp-state pp-adic Potts model on a Cayley tree

This work is devoted to description of all translation-invariant $p$-adic Gibbs measures for the $q$-state Potts model on a Cayley tree. In particular for the Cayley tree of order three we give exact number of such measures.Comment: arXiv admin note: text overlap with arXiv:1310.6220, arXiv:math-ph/0510025, arXiv:1208.3366, arXiv:1011.1395, arXiv:1107.4884, arXiv:0705.0244, arXiv:1402.6150 by other author

On pp-adic Gibbs measures for the SOS model on a Cayley tree

We consider $m+1$-state $p$-adic SOS model on a Cayley tree of order $k$.Comment: arXiv admin note: substantial text overlap with arXiv:1402.6150, arXiv:1402.717

On unconventional limit sets of contractive functions on Zp\mathbb Z_p

In the present paper, we are going to study metric properties of unconventional limit set of a semigroup $G$ generated by contractive functions $\{f_{i}\}_{i=1}^N$ on the unit ball $\mathbb Z_p$ of $p$-adic numbers. Namely, we prove that the unconventional limit set is compact, perfect and uniformly disconnected. Moreover, we provide an example of two contractions for which the corresponding unconventional limiting set is quasi-symmetrically equivalent to the symbolic Cantor set.Comment: 14 page

Translation-invariant Gibbs measures for the Blum-Kapel model on a Cayley tree

In this paper we consider translation-invariant Gibbs measures for the Blum-Kapel model on a Cayley tree of order k. An approximate critical temperature T_{cr} is found such that for T\geq T_{cr} there exists a unique translation-invariant Gibbs measure and for 0<T<T_{cr} there are exactly three translation-invariant Gibbs measures. In addition, we studied the problem of (not) extremality for the unique Gibbs measure.Comment: in Englis

Description of all translation-invariant pp-adic Gibbs measures for the Potts model on a Cayley tree

Recently it was proved that usual (real) Potts model on a Cayley tree has up to $2^q-1$ translation-invariant Gibbs measures. This paper is devoted to description of translation- invariant $p$-adic Gibbs measures (TIpGMs) of the $p$-adic Potts model. In particular, for the Cayley tree of order two we give exact number of such measures. Mereover we give criterion of boundedness of TIpGMs.Comment: 23 page

Weakly periodic Gibbs measures for two and three state HC models on a Cayley tree

In this paper we study two and three state HC-model on a Cayley tree. Under some conditions on parameters of the HC-model, in the case of normal divisor of the index four, we prove the existence of the weakly periodic (non periodic) Gibbs measures which are different from the known weakly periodic measures. Moreover, we find some regions for the $\lambda$ parameter ensuring that a extreme measure is not unique

Gibbs measures and free energies of Ising-Vannimenus Model on the Cayley tree

In this paper, we consider the Ising-Vannimenus model on a Cayley tree for order two with competing nearest-neighbor and prolonged next-nearest neighbor interactions. We stress that the mentioned model was investigated only numerically, without rigorous (mathematical) proofs. One of the main points of this paper is to propose a measure-theoretical approach for the considered model. We find certain conditions for the existence of Gibbs measures corresponding to the model, which allowed to establish the existence of the phase transition. Moreover, the free energies and entropies, associated with translation invariant Gibbs measures, are calculated.Comment: 15 pages, 2 figures. arXiv admin note: text overlap with arXiv:1504.0075

Positive solutions of nonlinear integral equations and surjectivity of Non-Linear Markov Operators On Infinite Dimensional Simplex

In the present paper, we consider the solvability of positive solutions of nonlinear integral equations by means of investigating non-linear Markov operators. To solve the problem we find necessary and sufficient condition for the surjectivity of nonlinear Markov operators.Comment: 16 page

pp-adic quasi Gibbs measure for Vannimenus model on a Cayley tree

In this paper we study the boundedness of the $p$-adic quasi Gibbs measures for the Vannimenus model on a Cayley tree of order two.Comment: in Russia

On pp-adic Hard Sphere model with three states on a Cayley tree

We study $p$-adic model of hard spheres with three states on the Cayley tree. We show that there exist three translation-invariant $p$-adic Gibbs measures and two periodic measures on a Cayley tree of oreder two.Comment: in Russia