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 $χ\approx 0.75$ for the number of particles in defect simulations and $χ\approx 0.5$ 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, $β/ν_\perp = 0.5000(6)$. Our numerical results for $β/ν_\|$ and $z$ are clearly different from the conjectured rational numbers $β/ν_\| = \frac{2}{7} \approx 0.2857$, $z = \frac{7}{4}= 1.75$ by Jensen [Phys. Rev. E, {\bf 50}, 3623 (1994)]. Our result for $β/ν_\perp$, however, is consistent with $\frac{1}{2}$, which is believed to be exact.

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