相关论文: On Ground States and Phase Transitions of $\lambda…

In the present paper, we study the $(2,q)$-Ising-Potts model on the Cayley tree. We have derived a recurrence equation that shows the existence of a splitting Gibbs measure for this model. Furthermore, we have proven that for the…

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…

Work is a continuation of work TMPh, 175(2), 2013. We study the Potts model with zero external field on the Cayley tree. It is shown that for any values of the parameter all periodic Gibbs measures are translation-invariant for the q-state…

We consider Potts model, with competing interactions and countable spin values $\Phi=\{0,1,\dots \}$ on a Cayley tree of order three. We study periodic ground states for this model.

The work is devoted to gradient Gibbs measures (GGMs) of a SOS model with countable set $\mathbb Z$ of spin values and having alternating magnetism on Cayley trees. This model is defined by a nearest-neighbor gradient interaction potential.…

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a…

The paper concerns the $q$-state Potts model (i.e., with spin values in $\{1,\dots,q\}$) on a Cayley tree $\mathbb{T}^k$ of degree $k\geq 2$ (i.e., with $k+1$ edges emanating from each vertex) in an external (possibly random) field. We…

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…

In the present paper we consider countable state $p$-adic Potts model on the Cayley tree. A construction of $p$-adic Gibbs measures which depends on weights $\l$ is given, and an investigation of such measures is reduced to examination of…

We consider a nearest-neighbor solid-on-solid (SOS) model, with several spin values $0,1,2,...,m, m\geq2$ and non zero external field, on a Cayley tree of order $k$. In the case $k=2, m=2$, we describe translation-invariant ground states…

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…

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…

For SOS (solid-on-solid) model with external field and with spin values from the set of all integers, on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corresponds to a boundary law (a function defined on vertices of…

We present a class of optimum ground states for spin-3/2 models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5 continuous parameters. For all values of these parameters the…

We consider an SOS (solid-on-solid) model, with spin values from the set of all integers, on a Cayley tree of order k and are interested in translation-invariant gradient Gibbs measures (GGMs) of the model. Such a measure corresponds to a…

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…

In this paper, we consider the Ising-Vanniminus model on an arbitrary order Cayley tree. We generalize the results conjectured in [Chinese Journal of Physics, 54 (4), 635-649 (2016)] and [International Journal of Modern Physics,…

We consider a nearest-neighbor solid-on-solid (SOS) model, with several spin values $0,1,\ldots,m,$ $m\geq2,$ and nonzero external field, on a Cayley tree of degree $k$ (with $k+1$ neighbors). We are aiming to extend the results of…

We consider nearest-neighbor fertile hard-core models, with three states, on a homogeneous Cayley tree. It is known that there are four type of such models. We investigate all of them and describe translation-invariant and periodic…

In the paper the Ising model with competing $J_1$ and $J_2$ interactions with spin values $\pm 1$, on a Cayley tree of order 2 (with 3 neighbors) is considered . We study the structure of the ground states and verify the Peierls condition…