Non-universal finite size scaling of rough surfaces

We demonstrate the non-universal behavior of finite size scaling in (1+1) dimension of a nonlinear discrete growth model involving extended particles in generalized point of view. In particular, we show the violation of the universal nature of the scaling function corresponding to the height fluctuation in (1+1) dimension. The 2nd order moment of the height fluctuation shows three distinct crossover regions separated by two crossover time scales namely, tx1 and tx2. Each regime has different scaling property. The overall scaling behavior is postulated with a new scaling relation represented as the linear sum of two scaling functions valid for each scaling regime. Besides, we notice the dependence of the roughness exponents on the finite size of the system. The roughness exponents corresponding to the rough surface is compared with the growth rate or the velocity of the surface.