First-order phase transition and tricritical scaling behavior of the Blume-Capel model: a Wang-Landau sampling approach

We investigate the tricritical scaling behavior of the two-dimensional spin-$1$ Blume-Capel model using the Wang-Landau method measuring the joint density of states for lattice sizes up to $48\times 48$ sites. The first-order transition curve is systematically determined employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. Deep in the first-order area of the phase diagram, we also find that the specific heat exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. At the tricritical point, we characterize the tricritical exponents through finite-size scaling analysis including the phenomenological finite-size scaling with thermodynamic variables. Our estimation of the tricritical eigenvalue exponents, $y_t = 1.804(5)$, $y_g = 0.80(1)$, and $y_h = 1.925(3)$, provides the first Wang-Landau verification of the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.