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The first order phase transition of the three-dimensional Blume Capel areinvestigated using cooling algorithm which improved from Creutz CellularAutomaton for the $D/J=2.9$ parameter value in the first order phase transitionregion. The analysis of the data using the finite-size effect and the histogramtechnique indicate that the magnetic susceptibility maxima and the specificheat maxima increase with the system volume ($L^{d}$) at $% D/J=2.9$.Comment: 13 pages, 4 figure

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