The mixed spin-2 and spin-52 Blume–Emery–Griffiths (BEG) Ising ferrimagnetic system is studied on the Bethe lattice using the exact recursion equations with the coordination number q=3 corresponding to the honeycomb lattice on real lattices. The influences of the crystal field and the...

We analyze the spectra of eigenvalues for random graphs with a local tree-like structure. The exact equations to the spectra of networks with a local tree-like structure are presented. We propose a simple approximation, and in the framework of effective medium approximation, calculate spectra of...

The stationary states of the kinetic spin-1 Blume–Capel (BC) model on the Bethe lattice are analyzed in detail in terms of recursion relations. The model is described using a Glauber-type stochastic dynamics in the presence of a time-dependent oscillating external magnetic field (h) and...

The approach developed by Thompson for the Ising model is used to calculate the free energy of the Potts model on the Bethe lattice. This is accomplished by introducing a simplification in obtaining the recursion relationship for the local magnetization and a generalization of the hyperbolic...

The possibility of a diffuse interface of an Ising model on a Cayley tree with four nearest neighbors is illustrated using the unstable solution of the one-phase problem. The pinning of the domain wall is caused by a weakening influence from this solution in favor of the bulk one.

A mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration–iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total and sublattice magnetizations are obtained from a...

The lattice spin model with Q-component discrete spin variables restricted to have orientations orthogonal to the faces of Q-dimensional hypercube is considered on the Bethe lattice, the recursive graph which contains no cycles. The partition function of the model with dipole–dipole and...

Exact expressions for the magnetization or the dipole moment, the quadrupolar moment and the Curie temperature of the spin-3/2 Blume–Capel model on the Bethe lattice are derived using the recursion method. The thermal variations of the magnetization and quadrupolar moment order parameters are...

The phase diagrams of the bilayer spin-32 Ising model on the Bethe lattice is analyzed by taking into account the intralayer coupling constants of the two layers (J1,J2), interlayer coupling constant between the layers (J3) and crystal field interaction (D) for the coordination number q=3 by...

We develop a transfer matrix method to compute exactly the spin–spin correlation functions for Bethe lattice Ising model and Blume–Emery–Griffiths (BEG) model in the external magnetic field h and for any temperature T. The correlation length ξ(T,h) obtained from the spin–spin...