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

Abstract

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 (Delta) 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. The positions of the tricritical point in the phase diagram are determined as [Delta(t)/J = 2.978(1); k(B)T(t)/J = 0.439(1)] and [Delta(t)/J = 3.949(1); k(B)T(t)/J = 0.854(1)] for the simple cubic and the body-centered cubic lattices, respectively. A very strong supercritical slowing down and hysteresis were observed in the Metropolis update close to first-order transitions for Delta > Delta(t) in the body-centered cubic lattice. In addition, for both lattices we found a line of compensation points, where the two sublattice magnetizations have the same magnitude. We show that the compensation lines are also S independent.