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

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 92; no. 2; p. 022134
• Main Authors: Kwak, Wooseop, Jeong, Joohyeok, Lee, Juhee, Kim, Dong-Hee
• Format: Journal Article
• Language: English
• Published: United States 24-08-2015
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/physreve.92.022134

We investigate the tricritical scaling behavior of the two-dimensional spin-1 Blume-Capel model by using the Wang-Landau method of measuring the joint density of states for lattice sizes up to 48×48 sites. We find that the specific heat deep in the first-order area of the phase diagram exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. The first-order transition curve is systematically determined by employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. 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, yt=1.804(5), yg=0.80(1), and yh=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.