The effect of the heating rate on the order to order phase transition

The simple cubic spin-1 Ising (BEG) model exhibits the ferromagnetic (F) - ferromagnetic (F) phase transition at low temperature region for the interval 1.40<d=D/J<1.48 at k=K/J=-0.5. The degree of the F-F phase transtion determines the special point on the (kT/J, d) phase diagram In this paper, the critical behavior of the ferromagnetic (F) - ferromagnetic (F) phase transition has been investigated for different heating rates using the cellular automaton (CA) heating algorithm. The variations with heating rate for the F-F phase transition order are quite important at the creation of phase diagrams. Therefore, the universality class and the type of ferromagnetic (F) - ferromagnetic (F) phase transition have been researched using the finite - size scaling theory, the power law relations and the probability distributions. The results show that the F-F phase transition can be the second order, the first order or the weak first order depending on the heating rate in the interval 1.40<d<1.48 for k=-0.5.