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

The long wavelength scaling properties of the Kardar-Parisi-Zhang equa tion have been studied using a field-theory renormalization technique. The perturbation expansions are carried out to two-loop order for bot h 1 + 1 and 2 + 1 dimensions. In substrate dimension d = 1, we find th at the perturbation formalism obeys the fluctuation-dissipation theore m order by order so that the exact results chi = 1/2, z = 3/2 are reco vered in every order. For substrate dimension d = 2, which is the crit ical dimension of this equation, an infrared stable strong coupling fi xed point is found and the dynamic scaling exponents of this fixed poi nt 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 determi ned by simulations of discrete models. The possible reasons for this d iscrepancy are discussed.