A thermodynamically self-consistent theory for the Blume-Capel model

Details A thermodynamically self-consistent theory for the Blume-Capel model A thermodynamically self-consistent theory for the Blume-Capel model

2000-11-02

arxiv.org/abs/cond-mat/0011048v1

Physics

Condensed Matter

Statistical Mechanics

11 figures. to appear in Physical Review E

Scientific paper

10.1103/PhysRevE.63.041111

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 partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in non-zero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the $\lambda$-line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.

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