E. Frey et Uc. Tauber, 2-LOOP RENORMALIZATION-GROUP ANALYSIS OF THE BURGERS-KARDAR-PARISI-ZHANG EQUATION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(2), 1994, pp. 1024-1045
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 us
e the dimensional regularization scheme, carefully keeping the full d
dependence originating from the angular parts of the loop integrals. F
or dimensions less than d(c) = 2 we find a strong-coupling fixed point
, which diverges at d = 2, indicating that there is nonperturbative st
rong-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 approxi
mation, and the two-loop contributions to the scaling functions are no
nsingular. For d > 2 dimensions, there is no finite strong-coupling fi
xed point. In the framework of a 2 + epsilon expansion, we find the dy
namic exponent corresponding to the unstable fixed point, which descri
bes 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 corre
lation length exponent at the transition is 1/nu = epsilon + O(epsilon
3) . For the smooth phase, some aspects of the crossover from Gaussian
to critical behavior are discussed.