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- W2020716303 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 $2+epsilon$ expansion, we find the dynamic exponent corresponding to the unstable fixed point, which describes the non--equilibrium roughening transition, to be $z = 2 + {cal O} (epsilon^3)$, in agreement with a recent scaling argument by Doty and Kosterlitz. Similarly, our result for the correlation length exponent at the transition is $1/nu = epsilon + {cal O} (epsilon^3)$. For the smooth phase, some aspects of the crossover from Gaussian to critical behavior are discussed." @default.
- W2020716303 created "2016-06-24" @default.
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- W2020716303 date "1994-08-01" @default.
- W2020716303 modified "2023-10-10" @default.
- W2020716303 title "Two-loop renormalization-group analysis of the Burgers–Kardar-Parisi-Zhang equation" @default.
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- W2020716303 doi "https://doi.org/10.1103/physreve.50.1024" @default.
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