Monte Carlo simulations of the Blume-Emery-Griffiths model with S=3/2 and S=5/2

► The MC simulation for the S=3/2 and 5/2 BEG model on the square lattice. ► The ground state phase diagrams are obtained. ► We investigate the spin structure and the temperature dependences of magnetization. ► The abnormal behaviors of magnetization are explained by sublattice magnetization.