The general-spin Blume-Capel model: A study of the multicritical behavior using effective-field theory

The general-spin Blume-Capel model is studied by using an effective-field theory with correlation. An expression for the free energy within the effective-field theory is proposed, and the complete phase diagram is constructed in the temperature and single-ion anisotropy plane. The first-order transition lines are obtained by Maxwell construction (comparison between free energies). Beyond first-order transitions at low temperatures, the results show second-order transitions and tricritical points, as well as a variety of double critical endpoints. The existence of the tricritical point and the number of critical endpoints strongly depend on the value of the spin.