Nonperturbative renormalization group for the Kardar-Parisi-Zhang equation

We present a method, rooted in the non-perturbative renormalization 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 implement an approximation scheme and show that it yields a complete, qualitatively correct phase diagram in all physical dimensions with reasonable values for the critical exponents. We also compute in one dimension the full (momentum and frequency dependent) correlation function, and the associated universal scaling functions. We find an excellent quantitative agreement with the exact results from Praehofer and Spohn (2004). This result is generalized in 2+1 en 3+1 predicting correlation and response functions. Associated universal amplitude ratios were predicted and have after been successfully confirmed by lattice simulations (Halpin-Healy, 2013). Generalizations as the inclusion of anisotropies or long-range correlated noise are discussed. Finally, preliminary results in order to improve the approximation in order to analyze the four and higher dimensional behavior is also discussed. The presented work is based on the references Phys. Rev. Lett. 104 (2010) 150601; Phys. Rev. E84 (2011) 061128; Phys. Rev. E86 (2012) 051124; Phys. Rev. E89 (2014) 2, 022108; Phys. Rev. E90 (2014) 6, 062133,