Static Approach to Renormalization Group Analysis of Stochastic Models with Spatially Quenched Noise

A new “static” renormalization group approach to stochastic models of fluctuating surfaces with spatially quenched noise is proposed in which only time-independent quantities are involved. As examples, quenched versions of the Kardar–Parisi–Zhang model and its Pavlik’s modification, the Hwa–Kardar model of self-organized criticality, and Pastor–Satorras–Rothman model of landscape erosion are studied. It is shown that the logarithmic dimension in the quenched models is shifted by two units upwards in comparison to their counterparts with white in-time noise. Possible scaling regimes associated with fixed points of the renormalization group equations are found and the critical exponents are derived to the leading order of the corresponding ε expansions. Some exact values and relations for these exponents are obtained.