Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications

Details Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications

2011-07-12

arxiv.org/abs/1107.2289v2

Phys. Rev. E 84, 061128 (2011)

Physics

Condensed Matter

Statistical Mechanics

18 pages, 6 figures, revised version prior to publication

Scientific paper

We present an analytical method, rooted in the non-perturbative renormalisation group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all its different regimes, including the strong-coupling one. We analyze the symmetries of the KPZ problem and derive an approximation scheme that satisfies the linearly realized ones. We implement this scheme at the minimal order in the response field, and show that it yields a complete, qualitatively correct phase diagram in all dimensions, with reasonable values for the critical exponents in physical dimensions. We also compute in one dimension the full (momentum and frequency dependent) correlation function, and the associated universal scaling function. We find good quantitative agreement with the exact result from Praehofer and Spohn. In particular, we obtain, for the universal amplitude ratio, $g_0\simeq 1.13(2)$, to be compared with the exact value $g_0=1.1504...$ (the Baik-Rain constant). We emphasize that all these results, which can be systematically improved, are obtained with sole input the bare action and the symmetries, without further assumptions on the existence of scaling or on the form of the scaling function.

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