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

TL;DR

This study uses Wang-Landau sampling to analyze the tricritical behavior of the 2D Blume-Capel model, accurately determining phase transition points and critical exponents, confirming conjectured values and revealing complex specific heat features.

Contribution

It provides the first Wang-Landau-based verification of tricritical exponents in the model, demonstrating the method's effectiveness for multicritical phenomena analysis.

Findings

Accurate determination of the first-order transition curve.

Observation of double-peak specific heat structure.

Estimation of tricritical exponents matching conjectured values.

Abstract

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.