FIELD-THEORY RENORMALIZATION APPROACH TO THE KARDAR-PARISI-ZHANG EQUATION

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 chi = 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 X congruent-to 0.16, z congruent-to 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.