Interfaces with superroughness

We undertake an extensive analytical study of the (1+1)-dimensional discrete superrough growth processes, which are the growth processes with the global roughness exponent larger than 1. First, we obtain the exact expressions of the global interfacial width w(L,t), the local interfacial width relative to the substrate orientation w(l,t), and the local interfacial width relative to the local interfacial orientation w(n)(l,t), in terms of the equal-time height difference correlation functions G(r,t). These relations are exact and can be applied to all the (1+1)-dimensional discrete growth processes with periodic boundary conditions. Moreover, we show that the local roughness exponent must be smaller than 1 for the (1+1)-dimensional superrough growth processes with w(n)(l,t) retaining the same anomalous dynamic scaling behaviors as w(l,t); in contrast, the local roughness exponent must be equal to 1 for those with w(n)(l,t) retrieving the ordinary dynamic scaling behaviors.