Tricritical point in the mixed-spin Blume-Capel model on three-dimensional lattices: Metropolis and Wang-Landau sampling approaches.

We investigate the mixed-spin Blume-Capel model with spin-1/2 and spin-S (S=1, 2, and 3) on the simple cubic and body-centered cubic lattices with single-ion-splitting crystal field (Δ) by using the Metropolis and the Wang-Landau Monte Carlo methods. We show that the two methods are complementary: The Wang-Landau algorithm is efficient to construct phase diagrams and the Metropolis algorithm allows access to large-sized lattices. By numerical simulations, we prove that the tricritical point is independent of S for both lattices.