Growth exponents in a surface model with probabilistic diffusion

Surface growth models are nonequilibrium systems because they present flux of particles toward the surface of some substrate. These particles are deposited and form a thin film. The mean height and the roughening are physical quantities of interest because they give information about the growth of the film and its mildness. These physical quantities obeys power laws and the more interesting is the roughening power low. In the thermodynamic limit the roughening evolves as $\omega\sim t^{\beta}$ and, for long times, the roughening depends on the system size as $\omega\sim L^{\alpha}$. The Family - Vicsek scaling relation allows one to obtain these asymptotic forms. There are different deposition models, as the ballistic deposition model, the Eden model and solid on solid models as well as different relaxation mechanisms. In the present work, we consider the random sequential adsorption and we allow the deposited particle to diffuse to the nearest neighbour site that has the lowest height. However, the diffusion occurs with some probability $\lambda$ and we are interested in the effect of this probability on the exponents $\beta$ and $\alpha$. By employing Monte Carlo simulations and finite size scaling, we show that the exponent $\beta$ depends on the values of the probability $\lambda$.