Comment on “Dependence of asymptotic decay exponents on initial condition and the resulting scaling violation”

We present the mapping relation between a one-dimensional conserved lattice gas model and a two species reaction $A+B\to 0$. From the kinetics of $A+B\to 0$, we show that the anomalous critical decay of an order parameter in the conserved lattice gas model results from finite-size effects induced by the domain structure for random initial conditions where the scaling relation $z={\nu }_{\parallel }/{\nu }_{\perp }$ is violated. A simple initial condition satisfying the scaling relation is also discussed.

Figure 1

The scaling plots for random initial conditions at $\rho =1/2$. (a) Plot of ${\rho }_a{t}^{0.25}$ vs $t/L^2$ for ${\tau }_{\ell }$. Each line denotes the data of $L=512,1024,2048$ from top to bottom. (b) Plot of ${\rho }_{a}L/2$ vs $t/\left(L^2{log}_{10}L\right)$ for ${\tau }_o$. Inset shows the plot of ${\rho }_{a}L/2$ vs $t/L^2$. Each line denotes the data of $L=2048,1024,512$ from top to bottom.