Related papers: Periodic and Weakly Periodic Ground States for the…
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…
In this present paper, the recurrence equations of an Ising model with three coupling constants on a third-order Cayley tree are obtained. Paramagnetic and ferromagnetic phases associated with the Ising model are characterized. Types of…
This paper provides a local and global Calder\'on-Zygmund type estimate of a weak solution to the parabolic double-phase system. The proof of local estimate is based on comparison estimates and the scaling invariant property of the…
We introduce a function of the density of states for periodic Jacobi matrices on trees and prove a useful formula for it. This allows new, streamlined proofs of the gap labeling and Aomoto index theorems. We prove a version of this new…
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…
This work is devoted to description of all translation-invariant $p$-adic Gibbs measures for the $q$-state Potts model on a Cayley tree. In particular for the Cayley tree of order three we give exact number of such measures.
We study the Ising model on a Cayley tree. A wide class of new Gibbs states is exhibited.
In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the…
We introduce a new two-dimensional model with diagonal four spin exchange and an exactly knownground-state. Using variational ansaetze and exact diagonalisation we calculate upper and lower bounds for the critical coupling of the model.…
In this paper, we consider a Hard-Core $(HC)$ model with two spin values on Cayley trees. The conception of alternative Gibbs measure is introduced and translational invariance conditions for alternative Gibbs measures are found. Also, we…
We consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of…
We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for a class of external fields, asymptotically approaching a…
We consider both Hard-Core and Soft-Core Widom-Rowlinson models with spin values $-1,0,1$ on a Cayley tree of order $k\geq 2$ and we are interested in the Gibbs measures of the models. The models depend on 3 parameters: the order $k$ of the…
A space-periodic ground state is shown to exist for lattices of smeared ions in $\R^3$ coupled to the Schr\"odinger and scalar fields. The elementary cell is necessarily neutral. The 1D, 2D and 3D lattices in $\R^3$ are considered, and a…
We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap, and focus on states at the Lowest Landau Level (LLL). At linear order in the coupling parameter $g$, we exploit the rich…
Weak topological phases are usually described in terms of protection by the lattice translation symmetry. Their characterization explicitly relies on periodicity since weak invariants are expressed in terms of the momentum-space torus. We…
We study the interaction of a ground state with a class of trapping potentials. We track the precise asymptotic behavior of the solution if the interaction is weak, either because the ground state moves away from the potential or is very…
The purpose of this paper is to investigate the ground-state properties of two-dimensional Heisenberg models on a square lattice with a given dimerization. Our aim is threefold: First, we want to investigate the dimensional transition from…
We consider fertile HC-models with three states on a Cayley tree. It is known that four types of such models exist. For these models we describe the translation-invarinat Gibbs measures on a Cayley tree of order three.
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…