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

초록

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) similar to t(beta) with the growth exponent beta 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.

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