Thermodynamically self-consistent theory for the Blume-Capel model - art. 041111

We use a self-consistent Ornstein-Zernike approximation to study the Blume- Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partia l differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundar ies in a nonzero magnetic field. In particular, the coordinates of the tric ritical point are in very good agreement with the best estimates from simul ation or series expansion. Numerical and analytical analysis strongly sugge st that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior gov erned by mean-field exponents.