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

There are several examples which show that the critical exponents can be dependent on initial condition of the system. In such situations, there are many systems where various issues related to the universal behavior e.g. existence of universality, splitting of universality class, scaling violation, whether the initial dependence should persist even after sufficiently long time or is a transient effect, the reasons for such features, etc. are not yet quite clear. In this article, with the simple example of conserved lattice gas (CLG) model, we investigate such issues and clearly show that under certain situations the asymptotic decay exponents are in fact dependent on the initial condition of the system. We show that such effect arises because of existence of two competing time scales, and identify the initial conditions which capture the universal features of the system.