The study of the critical behaviour of spin-1 Ising model for the four dimensional hypercubic lattice on the cellular automaton

In this study, Spin-1 Ising Blume-Emery-Griffiths (BEG) model has been simulated by using a cellular automaton (CA) cooling algorithm improved from the 3-dimensional BEG model algorithm for the 4-dimensional hypercubic lattices. The simulations are done the simple hypercubic lattice, which the lattice size is L=18, with the periodic boundary condition through 1 000 000 cellular automaton step time. The calculations were carried out through the ?/J = -1, 0, 1 lines. The phase structure of the model was determined by means of the variation curves of the termodinamic quantities with the temperature. The 4-dimensional BEG model has ferromagnetic (F), quadrupole (Q), staggered quadrupole (SQ) and the dense ferromagnetic ordering regions. Nevertheless, the model exhibits the successive, reentrant ad multiple phase transitions and has the critical point, the bicritical point, the tricritical point, zero-temperature critical point and the critical end point for the various k parameters. The static critical were calculated by the logoritmic corrections to power law. These values are in agreement with the exponents of the Mean-field theory and with other teoric values. Furthermore, The universality of the 4-dimensional BEG model was obtained from analyzing data of the finite size scaling.Keywords : Spin-1 Ising model, Blume-Emery-Griffiths model, cellular automaton, cooling algorithm, heating algorithm, phase transitions, four dimensional hypercubic lattice, finite size scaling theory.