Abstract
The spin-1 Blume–Capel model with a random crystal field on a square lattice is studied by using an effective-field theory with correlation. We go beyond the standard formalism and analyze the first-order phase transitions using the free energy functional deduced from the equation of state. The complete phase diagram is constructed in the temperature and single-ion anisotropy amplitude plane. The first-order transition line is obtained by comparison between free energies. Our results predict first-order transition at low temperature and large anisotropy strengths.
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