High-precision estimate of the critical exponents for the directed Ising universality class

With extensive Monte Carlo simulations, we present high-precision estimates of the critical exponents of branching annihilating random walks with two offspring, a prototypical model of the directed Ising universality class in one dimension. To estimate the exponents accurately, we propose a systematic method to find corrections to scaling whose leading behavior is supposed to take the form t−χ in the long-time limit at the critical point. Our study shows that χ ≈ 0.75 for the number of particles in defect simulations and χ ≈ 0.5 for other measured quantities, which should be compared with the widely used value of χ = 1. Using χ so obtained, we analyze the effective exponents to find that β/ν‖ = 0.2872(2), z = 1.7415(5), η = 0.0000(2), and accordingly, β/ν⊥ = 0.5000(6). Our numerical results for β/ν‖ and z are clearly different from the conjectured rational numbers β/ν‖ = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tfrac{2} {7} $\end{document} ≈ 0.2857, z = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tfrac{7} {4} $\end{document} = 1.75 by Jensen [Phys. Rev. E, 50, 3623 (1994)]. Our result for β/ν⊥, however, is consistent with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tfrac{1} {2} $\end{document}, which is believed to be exact.