Related papers: On Uniqueness of Gibbs Measures for $P$-Adic Nonho…

In the paper we considere three state $p$-adic Potts model with competing interactions on a Cayley tree of order two. We reduce a problem of describing of the $p$-adic Gibbs measures to the solution of certain recursive equation, and using…

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 $p$-adic Potts (with $q\geq 2$ spin values and coupling constant $J\in \Q_p$) model on the Cayley tree of order $k\geq 1$. It is proved that a phase transition occurs at $k=2$, $q\in p\mathbb{N}$ and $p\geq 3$…

We consider a nearest-neighbor inhomogeneous $p$-adic Potts (with $q\geq 2$ spin values) model on the Cayley tree of order $k\geq 1$. The inhomogeneity means that the interaction $J_{xy}$ couplings depend on nearest-neighbors points $x, y $…

In this paper, we continue an investigation of the $p$-adic Ising-Vannimenus model on the Cayley tree of an arbitrary order $k$ $(k\geq 2$). We prove the existence of $p$-adic quasi Gibbs measures by analyzing fixed points of…

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…

In this paper we consider a model with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k \geq 2$. To study translation-invariant Gibbs measures of the model we drive an nonlinear functional…

In this paper we consider a $p$-adic Ising model on the Cayley tree of order $k\geq 2$. We give full description of all $p$-adic translation-invariant generalized Gibbs measures for $k=3$. Moreover, we show the existence of phase transition…

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…

In this paper we consider a nearest-neighbor $p$-adic hard core (HC) model, with fugacity $\lambda$, on a homogeneous Cayley tree of order $k$ (with $k + 1$ neighbors). We focus on $p$-adic Gibbs measures for the HC model, in particular on…

In the present paper, the Ising model with mixed spin-(1,1/2) is considered on the second order Cayley tree. A construction of splitting Gibbs measures corresponding the model is given which allows to establish the existence of the phase…

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…

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 the present paper we provide a new construction of measure, called $p$-adic quasi Gibbs measure, for countable state of $p$-adic Potts model on the Cayley tree. Such a construction depends on a parameter $\frak{p}$ and wights. In…

In the paper, we consider the $\lambda$-model with spin values $\{1, 2, 3\}$ on the Cayley tree of order two. We first describe ground states of the model. Moreover, we also proved the existence of translation-invariant Gibb measures for…

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,…

In the present paper, we study a phase transition problem for the $q$-state $p$-adic Potts model over the Cayley tree of order three. We consider a more general notion of $p$-adic Gibbs measure which depends on parameter $\rho\in\bq_p$.…

Ising model with competing nearest-neighbors and prolonged next-nearest-neighbors interactions on a Cayley tree has long been studied but there are still many problems untouched. This paper tackles new Gibbs measures of Ising-Vannimenus…

In this paper we investigate generalized Gibbs measure (GGM) for $p$-adic Hard-Core(HC) model with a countable set of spin values on a Cayley tree of order $k\geq 2$. This model is defined by $p$-adic parameters $\lambda_i$, $i\in \mathbb…

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…