Abstract
The general spin-S Blume–Capel model is studied within two different approaches: the pair approximation for the free energy, and Monte Carlo simulations. The global phase diagram in the temperature-anisotropy plane is obtained for general values of S in the pair approximation and the results are qualitatively the same as those of the usual mean field theory. Special interest is given in the low temperature region of the phase diagram where a number of first-order lines emerge from a multiphase point at the ground state. Monte Carlo simulations for S=1, 3/2, and 2 on simple cubic lattices also confirm the general trend of the mean field like approach, and in the special S=3/2 case the present results are in disagreement with previous Monte Carlo simulations, as well as renormalization group calculations on corresponding two-dimensional lattices.
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