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

Wooseop Kwak, Joohyeok Jeong, Juhee Lee, Dong-Hee Kim

Published 2015-04-10Version 1

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 line of the first-order phase transitions and the location of the tricritical point are determined employing the method of field mixing in conjunction with finite-size scaling. We estimate the tricritical exponents from the phenomenological finite-size scaling analysis on thermodynamic variables as well as from the finite-size scaling with the probability distribution function of a relevant field-conjugate variable at the tricritical point. Our estimations of the tricritical eigenvalue exponents, $y_t = 1.804(5)$, $y_g = 0.80(1)$, and $y_h = 1.925(3)$, are in excellent agreement with the previous calculations based on different methods and the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.