$A+A \rightarrow \emptyset$ model with a bias towards nearest neighbor

We have studied $A+A \rightarrow \emptyset$ reaction-diffusion model on a ring, with a bias $ε$ $(0 \leq ε\leq 0.5)$ of the random walkers $A$ to hop towards their nearest neighbor. Though the bias is local in space and time, we show that it alters the universality class of the problem. The $z$ exponent, which describes the growth of average spacings between the walkers with time, changes from the value 2 at $ε=0$ to the mean-field value of unity for any non-zero $ε$. We study the problem analytically using independent interval approximation and compare the scaling results with that obtained from simulation. The distribution $P(k,t)$ of the spacing $k$ between two walkers (per site) is given by $t^{-2/z} f(k/t^{1/z})$ as expected; however, the scaling function shows different behaviour in the two approaches.

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