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...

Effect of uniaxial single-ion anisotropy upon magnetic properties of a mixed spin-1/2 and spin-S (S⩾1) Ising model on a bathroom tile (4–8) lattice is examined within the framework of an exact star-triangle mapping transformation. Particular attention is focused on the phase diagrams...

We consider a system consisting of two layers of Bethe lattices each with a branching ratio of q Ising spins. The layer with spin- 1/2 atoms interacting with the nearest-neighbor (NN) bilinear interaction J1 is laid over the top of the other with spin-1 atoms interacting with the bilinear NN...

We present the numbers of dimer–monomers Md(n) on the Sierpinski gasket SGd(n) at stage n with dimension d equal to two, three and four. The upper and lower bounds for the asymptotic growth constant, defined as zSGd=limv→∞lnMd(n)/v where v is the number of vertices on SGd(n), are derived...

We present the numbers of ice model configurations (with Boltzmann factors equal to one) I(n) on the two-dimensional Sierpinski gasket SG(n) at stage n. The upper and lower bounds for the entropy per site, defined as limv→∞lnI(n)/v, where v is the number of vertices on SG(n), are derived in...

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...