1 research outputs found
Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation
A systematic analysis of the Burgers--Kardar--Parisi--Zhang equation in
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 dependence originating
from the angular parts of the loop integrals. For dimensions less than
we find a strong--coupling fixed point, which diverges at , indicating
that there is non--perturbative strong--coupling behavior for all .
At our method yields the identical fixed point as in the one--loop
approximation, and the two--loop contributions to the scaling functions are
non--singular. For dimensions, there is no finite strong--coupling fixed
point. In the framework of a expansion, we find the dynamic
exponent corresponding to the unstable fixed point, which describes the
non--equilibrium roughening transition, to be ,
in agreement with a recent scaling argument by Doty and Kosterlitz. Similarly,
our result for the correlation length exponent at the transition is . For the smooth phase, some aspects of the
crossover from Gaussian to critical behavior are discussed.Comment: 24 pages, written in LaTeX, 8 figures appended as postscript,
EF/UCT--94/3, to be published in Phys. Rev. E