Related papers: On $p$-state $p$-adic Potts model on a Cayley tree

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…

The phase transition phenomenon is one of the central problems of statistical mechanics. It occurs when the model possesses multiple Gibbs measures. In this paper, we consider a three-state SOS (solid-on-solid) model on a Cayley tree. We…

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…

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…

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 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 fertile three-state Hard-Core (HC) models with the activity parameter $\lambda>0$ on a Cayley tree. It is known that there exist four types of such models: "wrench"\,, "wand"\,, "hinge"\, and "pipe"\,. In cases "wand"\, and…

We consider a nearest-neighbor $p$-adic $\l$-model with spin values $\pm 1$ on a Cayley tree of order $k\geq 1$. We prove for the model there is no phase transition and as well as the unique $p$-adic Gibbs measure is bounded if and only if…

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 paper we generalize results of paper [12] for a $q$- component models on a Cayley tree of order $k\geq 2$. We generalize them in two directions: (1) from $k=2$ to any $k\geq 2;$ (2) from concrete examples (Potts and SOS models) of…

We consider a version of the solid-on-solid model on the Cayley tree of order two in which vertices carry spins of value $0,1$ or $2$ and the pairwise interaction of neighboring vertices is given by their spin difference to the power $p>0$.…

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 this paper, we focus on studying non-probability Gibbs measures for a Hard Core (HC) model on a Cayley tree of order $k\geq 2$, where the set of integers $\mathbb Z$ is the set of spin values. It is well-known that each Gibbs measure,…

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 study the Ising model on a Cayley tree. A wide class of new Gibbs states is exhibited.

In this paper we complete the analysis of a statistical mechanics model on Cayley trees of any degree, started in [EsHaRo12,EsRo10,BoEsRo13,JaKuBo14,Bo17]. The potential is of nearest-neighbor type and the local state space is compact but…

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…

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 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…

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.…