Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation

Erwin Frey; Uwe Claus Täuber

doi:10.1103/PhysRevE.50.1024

paper

Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation

arXiv:cond-mat/9406068 · doi:10.1103/PhysRevE.50.1024

Abstract

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 non--perturbative strong--coupling behavior for all $d \geq 2$ . 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 non--singular. For $d > 2$ dimensions, there is no finite strong--coupling fixed point. In the framework of a $2 + ε$ expansion, we find the dynamic exponent corresponding to the unstable fixed point, which describes the non--equilibrium roughening transition, to be $z = 2 + O (ε^{3})$ , in agreement with a recent scaling argument by Doty and Kosterlitz. Similarly, our result for the correlation length exponent at the transition is $1/ ν = ε + O (ε^{3})$ . For the smooth phase, some aspects of the crossover from Gaussian to critical behavior are discussed.

24 pages, written in LaTeX, 8 figures appended as postscript, EF/UCT--94/3, to be published in Phys. Rev. E1

Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation

Abstract

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