Dynamical behaviour of two and three dimensional Blume capel model

In this study, two and three dimensional Blume Capel model are simulated using the algorithms which improved from the Creutz cellular automaton (CCA) for square and simple cubic lattices. The dynamical behaviour of the model has been investigated for tricritical, first order and second-order points of the (kTC/J, D/J) phase space. The calculations are carried out on square lattice LxL of linear dimension L= 20, 40, 60, 80 and 100 and simple cubic lattices LxLxL of linear dimension L= 8, 10, 12, 16, 18 and 20 with periodic boundary conditions. Results show that the model has the different dynamical behaviour on the special points. On the other hand the order parameter probability distribution for 2D and 3D Spin-1/2 and Spin-1 Ising Model are calculated at the critical temperature. The finite size scaling relation for the order parameter probability distribution is tested and verified numerically by the CCA simulation. The constants of the analytical function are estimated by fitting it to probability function obtained numerically at the finite size critical point. For the large finite size, the analytical function is described the universal shape of order parameter probability distribution function with the same a and different c constants for both models.