Non-perturbative renormalization group approach to surface growth

We present a recently introduced real space renormalization group (RG) appr oach to the study of surface growth. The method permits us to obtain the pr operties of the KPZ strong coupling fixed point, which is not accessible to standard perturbative field theory approaches. Using this method, and with the aid of small Monte Carlo calculations for systems of linear size 2 and 4, we calculate the roughness exponent in dimensions up to d = 8. The resu lts agree with the known numerical values with good accuracy. Furthermore, the method permits us to predict the absence of an upper critical dimension for KPZ contrarily to recent claims. The RG scheme is applied to other gro wth models in different universality classes and reproduces very well all t he observed phenomenology and numerical results. Intended as a sort of fini te size scaling method, the new scheme may simplify in some cases from a co mputational point of view the calculation of scaling exponents of growth pr ocesses. (C) 1999 Elsevier Science B.V. All rights reserved.