We have studied the Blume–Capel model by using the expanded Bethe–Peierls approximation. In this approximation, the system is taken as a group of chains composed of a central chain and its nearest-neighbor chains. The nearest-neighbor chains are in an effective field produced by the other...

We investigate the temperature dependence of the order parameters of the Blume–Capel model for zero magnetic field in the lowest approximation of the cluster variation method which is identical to the mean-field approximation. Besides the stable branches of the order parameters, we establish...

Starting from correlation identities for the Blume–Capel spin 1 systems and using correlation inequalities, we obtain rigorous upper bounds for the critical temperature. The obtained results improve over effective field type results.

The static critical exponents of the three-dimensional Blume–Capel model which has a tricritical point at D/J=2.82 value are estimated for the standard and the cooling algorithms which improved from Creutz cellular automaton. The analyses of the data using the finite-size scaling and power-law...

Spin correlation identities for the Blume–Capel model on Kagome lattice are derived and combined with rigorous correlation inequalities lead to upper bounds on the critical temperature. From the spin correlation identities the mean field approximation and the effective field approximation...

We study the metastability and nucleation of the Blume–Capel model on complex networks, in which each node can take one of three possible spin variables {−1,0,1}. We consider the external magnetic field h to be positive, and let the chemical potential λ vary between −h and h in a low...