Related papers: Gibbs measures for hardcore-SOS models on Cayley t…

There are many research works devoted to Gibbs measure for models on Cayley trees. Among these works, there are some works in which the general results are identical, but the considered models are various. In this article, we present the…

In this paper, we consider Ising-Vannimenus model on a Cayley tree for order two with competing nearest-neighbor, prolonged next-nearest neighbor interactions. We stress that the mentioned model was investigated only numerically, without…

We consider models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$. It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear…

We consider translation-invariant splitting Gibbs measures (TISGMs) for the $q$-state Potts model on a Cayley tree of order two. Recently a full description of the TISGMs was obtained, and it was shown in particular that at sufficiently low…

In the present paper we shall consider countable state $p$-adic Potts model on $Z_+$. A main aim is to establish the existence of the phase transition for the model. In our study, we essentially use one dimensionality of the model. To show…

In this paper we study the extremality of translation-invariant Gibbs measure for the HC-model on a Cayley tree. It is known that for this model the translation-invariant measure is unique. We give a new proof of this statement and found…

We review and propose to use of associated dynamical system to explore the phase transition phenomena in $p$-adic statistical mechanics setting, by means of the renormalization techniques. Main focus of the paper is the $p$-adic…

We show that the nearest neighbors Ising model on the Cayley tree exhibits new temperature driven phase transitions. These transitions holds at various inverse temperatures different from the critical one. They are depicted by a change in…

For the Ising model on Cayley trees we give a very wide class of new Gibbs measures. We show that these new measures are extreme under some conditions on the temperature. We give a review of all known Gibbs measures of the Ising model on…

We continue our study of the full set of translation-invariant splitting Gibbs measures (TISGMs, translation-invariant tree-indexed Markov chains) for the $q$-state Potts model on a Cayley tree. In our previous work \cite{KRK} we gave a…

In this paper, we consider the $\lambda$-model with nearest neighbor interactions and with competing Potts interactions on the Cayley tree of order-two. We notice that if $\lambda$-function is taken as a Potts interaction function, then…

In this paper we construct several models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 2$. We prove that each of the constructed model has at least two translational-invariant…

We consider a coupled Ising-Potts model on Cayley trees of order $ k \geq 2 $. This model involves spin vectors $ (s, \sigma) $, and generalizes both the Ising and Potts models by incorporating interactions between two types of spins: $s =…

In this present paper, it is proposed the renormalization techniques in the investigation of phase transition phenomena in $p$-adic statistical mechanics. We mainly study $p$-adic $\l$-model on the Cayley tree of order two. We consider…

In the present paper, we introduce a new kind of $p$-adic measures for $q+1$-state Potts model, called {\it $p$-adic quasi Gibbs measure}. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we…

We consider $\mathbb Z$-valued $p$-SOS-models with nearest neighbor interactions of the form $|\omega_v-\omega_w|^p$, and finite-spin ferromagnetic models on regular trees. This includes the classical SOS-model, the discrete Gaussian model…

For the Potts model on Cayley trees, a very wide class of new Gibbs measures is given. We give a review of all known Gibbs measures of the Potts model on trees and compare them with our new measures.

We consider the Ising model with competing interactions and a nonzero external field on the Cayley tree of order two. We describe ground states and verify the Peierls condition for the model. Using a contour argument we show the existence…

In this paper we consider one model with nearest-neighbor interactions and with the set $[0,1]$ of spin values on the Cayley tree of order three. Translation-invariant Gibbs measures for the model are studied. Results are proved by using…

We consider models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$. We study periodic Gibbs measures of the model with period two. For $k=1$ we show that there is no any…