ar X iv : c on d - m at / 9 80 91 28 v 1 8 S ep 1 99 8 Non perturbative renormalization group approach to surface growth

We present a recently introduced real space renormalization group (RG) approach to the study of surface growth. The method permits us to obtain the properties 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 results 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 growth models in different universality classes and reproduces very well all the observed phenomenology and numerical results. Intended as a sort of finite size scaling method, the new scheme may simplify in some cases from a computational point of view the calculation of scaling exponents of growth processes. The study of the non equilibrium dynamics of rough surfaces and interfaces is a topic of growing interest [1, 2, 3]. Many efforts have been devoted to single out the behaviors shared by apparently different growing phenomena. In this context the search of universality classes, permitting to categorize different models and systems of rough surfaces sharing the same scaling properties, is a central task. The main milestone in this direction is the Kardar-Parisi-Zhang equation (KPZ), which is the minimal Langevin equation capturing the essential physics of many different growing surfaces beyond the Gaussian linear (Edward-Wilkinson) theory [1, 2, 3]. It reads [4] ∂h(x, t) ∂t = ν∇ 2 h + λ 2 (∇h) 2 + η(x, t).