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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 withsingle-ion-splitting crystal-field ($\Delta$) by using the Metropolis and theWang-Landau Monte Carlo methods. By numerical simulations, we prove that thetricritical point is spin-independent for both lattices. The positions of thetricritical point in the phase diagram are determined as($\Delta_t/J=2.978(1)$; $k_B T_t/J=0.439(1)$) and ($\Delta_t/J=3.949(1)$; $k_BT_t/J=0.854(1)$) for the simple cubic and the body-centered cubic lattices,respectively. A very strong supercritical slowing down and hysteresis wereobserved in the Metropolis update close to first-order transitions for$\Delta>\Delta_t$. In addition, for both lattices we found a line ofcompensation points, where the two sublattice magnetizations have the samemagnitude. We show that the compensation lines are also spin-independent.

physical review. e

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