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

TL;DR

This study uses Monte Carlo simulations to analyze the spin dependence of the tricritical point in the mixed-spin Blume-Capel model on cubic lattices, revealing spin-independent tricritical points and compensation lines.

Contribution

It demonstrates that the tricritical point positions and compensation lines are independent of the spin magnitude in the model.

Findings

Tricritical points are spin-independent for both lattices.

Positions of tricritical points are numerically determined.

Strong supercritical slowing down observed near first-order transitions.

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. By numerical simulations, we prove that the tricritical point is spin-independent 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 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 spin-independent.