Ballistic deposition with memory: A new universality class of surface growth with a new scaling law

Motivated by recent experimental studies in microbiology, we suggest modifying the classic ballistic deposition model of surface growth, where the memory of a deposition at a site induces more depositions at that site or its neighbors. By studying the statistics of surfaces in this model, we obtain three independent critical exponents: the growth exponent $\beta =5/4$, the roughening exponent $\alpha =2$, and the new (size) exponent $\gamma =1/2$. The model requires modifying the Family-Vicsek scaling, resulting in the dynamical exponent $z=\frac{\alpha +\gamma }{\beta }=2$. This modified scaling collapses the surface width vs time curves for various lattice sizes. This previously unobserved universality class of surface growth could describe the surface properties of a wide range of natural systems.