2-LOOP RENORMALIZATION-GROUP ANALYSIS OF THE BURGERS-KARDAR-PARISI-ZHANG EQUATION

A systematic analysis of the Burgers-Kardar-Parisi-Zhang equation in d + 1 dimensions by dynamic renormalization-group theory is described. The fixed points and exponents are calculated to two-loop order. We use the dimensional regularization scheme, carefully keeping the full d dependence originating from the angular parts of the loop integrals. For dimensions less than d(c) = 2 we find a strong-coupling fixed point, which diverges at d = 2, indicating that there is nonperturbative strong-coupling behavior for all d greater-than-or-equal-to 2. At d = 1 our method yields the identical fixed point as in the one-loop approximation, and the two-loop contributions to the scaling functions are nonsingular. For d > 2 dimensions, there is no finite strong-coupling fixed point. In the framework of a 2 + epsilon expansion, we find the dynamic exponent corresponding to the unstable fixed point, which describes the nonequilibrium roughening transition, to be z = 2 + O(epsilon3), in agreement with a recent scaling argument by Doty and Kosterlitz, Phys. Rev. Lett. 69, 1979 (1992). Similarly, our result for the correlation length exponent at the transition is 1/nu = epsilon + O(epsilon3) . For the smooth phase, some aspects of the crossover from Gaussian to critical behavior are discussed.