Thermodynamically self-consistent theory for the Blume-Capel model

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

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 a nonzero magne...

Random-field Blume-Capel model: Mean-field theory.

Dynamical Blume { Capel Model : Competing Metastable States

Random-cluster representation of the Blume–Capel model

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume–Capel model. It has three parameters, a vertex parameter a, an edge parameter p, and a cluster weighting factor q. Stochastic comparisons of measures are developed for the ‘vertex marginal’ when q ∈ [1, 2], and the ‘edge marginal’ when q ∈ [1,∞). Taken in conjunction with arguments used earl...

Percolation between vacancies in the two-dimensional Blume-Capel model.

Using suitable Monte Carlo methods and finite-size scaling, we investigate the Blume-Capel model on the square lattice. We construct percolation clusters by placing nearest-neighbor bonds between vacancies with a variable bond probability p(b) . At the tricritical point, we locate the percolation threshold of these vacancy clusters at p(bc) =0.706 33 (6) . At this point, we determine the fracta...