Finite Size Effect for the First-Order Phase Transition of the Three-Dimensional Blume--Capel Model on a Cellular Automaton

The first-order phase transition of the three-dimensional Blume--Capel model is investigated using the cooling algorithm which is improved from Creutz Cellular Automaton at D/J=2.9, i.e. a ratio of single-ion anisotropy constant to bilinear interaction energy. We test the efficiency of the algorithm and obtain the finite-size effects at the first-order phase transition point. The transition temperature is estimated using the probability distributions of the order parameter and the energy. The analysis of data at the transition point indicates that the magnetic susceptibility and the specific heat maxima increase with the system value (L^d).