• DOI:10.1103/PhysRevE.89.022108
• Corpus ID: 27753353

Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group.

@article{Kloss2013KardarParisiZhangEW,
  title={Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group.},
  author={Thomas Kloss and L{\'e}onie Canet and Bertrand Delamotte and Nicol{\'a}s Wschebor},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={89 2},
  pages={
          022108
        }
}

• T. Kloss, L. Canet, +1 author N. Wschebor
• Published 20 December 2013
• Physics
• Physical review. E, Statistical, nonlinear, and soft matter physics

We investigate the scaling regimes of the Kardar-Parisi-Zhang (KPZ) equation in the presence of spatially correlated noise with power-law decay D(p) ∼ p(-2ρ) in Fourier space, using a nonperturbative renormalization group approach. We determine the full phase diagram of the system as a function of ρ and the dimension d. In addition to the weak-coupling part of the diagram, which agrees with the results from Europhys. Lett. 47, 14 (1999) and Eur. Phys. J. B 9, 491 (1999), we find the two fixed points describing the short-range- (SR) and long-range- (LR) dominated strong-coupling phases. In contrast with a suggestion in the references cited above, we show that, for all values of ρ, there exists a unique strong-coupling SR fixed point that can be continuously followed as a function of d. We show in particular that the existence and the behavior of the LR fixed point do not provide any hint for 4 being the upper critical dimension of the KPZ equation with SR noise.