Dynamic phase transitions in the kinetic Ising model on the Bethe lattice.

The stationary states of the kinetic Ising model described by the Glauber stochastic dynamics subject to a time-dependent oscillating external magnetic field was analyzed in detail on the Bethe lattice in terms of the recursion relation. The dynamic order parameter, the hysteresis loop area, and the dynamic correlation are calculated. It was found that the magnetization oscillates around nonzero values at low temperatures for the ferromagnetic phase while it only oscillates around zero values at high temperatures for the paramagnetic phase for appropriate values of the oscillating external magnetic field.

Crystal field effect on a bilayer Bethe lattice.

The influence of the crystal field on the phase diagrams of the bilayer spin-1 Ising model on the Bethe lattice is studied in terms of the intralayer coupling constants J1 and J2 of the two layers and interlayer coupling constant J3 between the layers for given values of the coordination number q by using the recursion relation scheme. The six distinct ground-state configurations of the model are obtained on the (J_{2}J_{1},J_{3}qJ_{1}) plane with J1>0 , the ferromagnetic coupling, for given values of the crystal field. Then, the phase diagram of the system is obtained on the (kTJ_{1},J_{3}J_{1}) plane for given values of the crystal field and alpha=J_{2}J_{1} with q=4 corresponding to the square lattice in real lattice systems.