Related papers: On some remarks on the Ising model with competing …
A BEG Hamiltonian is used to model an Ising spin glass with annealed vacancies on a hierarchical lattice. In addition to competing bilinear interactions, repulsive biquadratic interactions on the perimeter of our unit structures compete…
We study the interplay between a XY anisotropy $\gamma$, exchange modulations and an external magnetic field along the z direction in the XYZ chain using bosonization and Lanczos diagonalization techniques. We find an Ising critical line in…
Entanglement generated by Ising model has been studied for several authors in order to understand the relation between it and magnetic properties of materials, principally using one or two dimensional models for two or more particles. In…
For the Potts model on Cayley trees, a very wide class of new Gibbs measures is given. We give a review of all known Gibbs measures of the Potts model on trees and compare them with our new measures.
In this paper under some conditions on parameters of the Potts model with q-states on a Cayley tree of order k it is proved existence of the periodic (non translation-invariant)Gibbs measures. Also given a theorem about the number of these…
We consider the free boundary condition Gibbs measure of the Potts model on a random tree. We provide an explicit temperature interval below the ferromagnetic transition temperature for which this measure is extremal, improving older bounds…
The Ising one-dimensional (1D) chain with spin $S=1/2$ and magnetoelastic interactions is studied with the lattice contribution included in the form of elastic interaction and thermal vibrations simultaneously taken into account. The…
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…
Using an iteration technique, we obtain exact expressions for the free energy and the magnetization of an Ising model on a two - layer Bethe lattice with intralayer coupling constants J1 and J2 for the first and the second layer,…
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,…
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.
For arbitrary Ising-like models of any dimension and Hamiltonians with a finite support with all possible multispin interactions and boundary conditions with a shift, the exact value of the free energy in the thermodynamic limit is obtained…
We consider the SOS (solid-on-solid) model, with spin values $0,1,2$, on the Cayley tree of order two (binary tree). We treat both ferromagnetic and antiferromagnetic coupling, with interactions which are proportional to the absolute value…
Several recent experiments in biology study systems composed of several interacting elements, for example neuron networks. Normally, measurements describe only the collective behavior of the system, even if in most cases we would like to…
We analyze the ferromagnetic Ising model on a scale-free tree; the growing random network model with the linear attachment kernel $A_k=k+\alpha$ introduced by [Krapivsky et al.: Phys. Rev. Lett. {\bf 85} (2000) 4629-4632]. We derive an…
We investigate the mixed spin-$(s,\tfrac12)$ Ising model on a Cayley tree of order three ($k=3$), extending the approach of \cite{Akin2024}. For the representative case $s=5$, the associated recursion leads to an 11-dimensional dynamical…
An improved unified formulation based on the effective field theory is introduced for a spin-1 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the…
Inference in general Ising models is difficult, due to high treewidth making tree-based algorithms intractable. Moreover, when interactions are strong, Gibbs sampling may take exponential time to converge to the stationary distribution. We…
We consider a hard core (HC) model with a countable set $\mathbb{Z}$ of spin values on the Cayley tree. This model is defined by a countable set of parameters $\lambda_{i}>0, i \in \mathbb{Z}\setminus\{0\}$. For all possible values of…
In this paper we give a systematic review of the theory of Gibbs measures of Potts model on Cayley trees (developed since 2013) and discuss many applications of the Potts model to real world situations: mainly biology, physics, and some…