Phase transition of the restricted solid-on-solid model via deposition probabilities in higher dimensions

We consider a generalized restricted solid-on-solid (GRSOS) model in 6 + 1 and 11 + 1 dimensions. In the GRSOS model, particles are either deposited with a probability p or evaporated with a probability q = 1 - p . The nonlinearity of the model is expected to be proportional to the difference between evaporation and deposition probabilities, q - p , and controlled by adjusting the parameter p . For p = 1 , the surface width W ( L , t ) grows following the power-law behavior W ( t ) ∼ t β with the growth exponent β that is known in the Kardar–Parisi–Zhang (KPZ) universality class, where L and t are, respectively, the linear size of system and evolution time. In the equilibrium case of p = q = 1 2 , W ( L , t ) saturates to a constant in both 6 + 1 and 11 + 1 dimensions. In the nonequilibrium cases, W 2 ( t ) grows logarithmically with time t at the critical probability p c in both dimensions, with the value of p c being dependent on the dimensionality; the system thus exhibits a phase transition from a smooth phase to a rough phase at p c . Our results support that the critical dimension of the KPZ equation is higher than 11 + 1 or might not exist.