Dynamic phase transitions and dynamic compensation temperature in the mixed spin-1 and spin-2 ising model

The dynamic behavior of a mixed spin-1 and spin-2 Ising system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field on alternate layers of a hexagonal lattice is studied by using the Glauber-type stochastic dynamics. The set of mean-field dynamic equations is obtained by employing the Master equation and Glauber transitions rates. Firstly, the time variation of the average sublattice magnetizations is studied in order to find the phases in the system. Then, the thermal behavior of the dynamic sublattice magnetizations and dynamic total magnetization is investigated to obtain the dynamic phase transition points and dynamic compensation temperature. From these investigations, it is characterized the nature (continuous or discontinuous) of phase transitions and is found the type of compensation behavior. It is presented the dynamic phase diagrams for both presence and absence of the dynamic compensation temperature in the nine different planes. According to the values of Hamiltonian parameters, besides the paramagnetic (p), antiferromagnetic (af), ferrimagnetic (i) and nonmagnetic (nm) fundamental phases, eight different mixed phase regions which are composed of binary and ternary combinations of fundamental phase and the compensation temperature or L- and N-types compensation behavior exist in the system.