Field-theory renormalization approach to the Kardar-Parisi-Zhang equation

Abstract

The long wavelength scaling properties of the Kardar-Parisi-Zhang equation have been studied using a field-theory renormalization technique. The perturbation expansions are carried out to two-loop order for both 1+1 and 2+1 dimensions. In substrate dimension d=1, we find that the perturbation formalism obeys the fluctuation-dissipation theorem order by order so that the exact results χ=1/2, z=3/2 are recovered in every order. For substrate dimension d=2, which is the critical dimension of this equation, an infrared stable strong coupling fixed point is found and the dynamic scaling exponents of this fixed point are obtained to be χ≃0.16, z≃1.84, which are roughly halfway between the free field exponents and those determined by simulations of discrete models. The possible reasons for this discrepancy are discussed.