Related papers: On $p$-state $p$-adic Potts model on a Cayley tree
We consider the Ising model on a Cayley tree . For the Ising model found new weakly periodic measures corresponding normal subgroups of index 2 of the group representation of the tree Cayley.
In the present paper we continue the investigation from [1] and consider the SOS (solid-on-solid) model on the Cayley tree of order $k \geq 2$. In the ferromagnetic SOS case on the Cayley tree, we find three solutions to a class of period-4…
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.
In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We…
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 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 =…
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 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. These models arise as simple examples 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 investigate translation-invariant splitting Gibbs measures (TISGMs) for the HC-Blume-Capel model on a "wand" graph embedded in the Cayley tree of arbitrary order $k \geq 2$. It is known that there is the exact critical…
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…
For the Potts model on the Cayley tree, some explicit formulae of the free energies and entropies (according to vector-valued boundary conditions (BCs)) are obtained. They include translation-invariant, periodic, Dobrushin-like BCs, as well…
We consider Gradient Gibbs measures corresponding to a periodic boundary law for a generalized SOS model with spin values from a countable set, on Cayley trees. On the Cayley tree, detailed information on Gradient Gibbs measures for models…
We consider the Potts model with two-step interactions and spin values 1,2,3,4 on a Cayley tree. We describe periodic ground states and verify the Peierls condition for the model.
We consider the ferromagnetic n.n Ising model on Cayley trees in absence of external fields submitted to a modified majority rule transformation with overlapping cells already known to lead to non-Gibbsian measures. We describe the…
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…
For the $q-$state Potts model new order parameters projecting on a group of spins instead of a single spin are introduced. On a Cayley tree this allows the physical interpretation of the Potts model at noninteger values q of the number of…
In this note, we give a nature action of the modular group on the ends of the infinite (p + 1)-cayley tree, for each prime p. We show that there is a unique invariant probability measure for each p.
We prove that all Gibbs measures of the $q$-state Potts model on $\mathbb{Z}^2$ are linear combinations of the extremal measures obtained as thermodynamic limits under free or monochromatic boundary conditions. In particular all Gibbs…
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…