Anomalous scaling of superrough growing surfaces: from correlation functions to residual local interfacial widths and scaling exponents.

A study on the (1+1) -dimensional superrough growth processes is undertaken. We first work out the exact relations among the local interfacial width w , the correlation function G , and the pth degree residual local interfacial width w(p) with p=1,2,3,... . The relations obtained are exact and thus can be applied to any (1+1) -dimensional growth processes in the continuum limit, no matter whether the interface is superrough or not. Then we investigate the influence of the macroscopic structure formation on the scaling behavior of the superrough growth processes. Moreover, we show analytically that the residual local interfacial width w(p) excludes only the influence of the macroscopic structure on the scaling behavior of the system and retains the true scaling behavior originating from the stochastic nature of the system. Finally, we analyze and simulate some superrough growth models for demonstration.