Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: Scaling functions and amplitude ratios in 1+1, 2+1, and 3+1 dimensions

We investigate the strong-coupling regime of the stationary Kardar-Parisi-Zhang equation for interfaces growing on a substrate of dimension d = 1, 2, and 3 using a nonperturbative renormalization group (NPRG) approach. We compute critical exponents, correlation and response functions, extract the related scaling functions, and calculate universal amplitude ratios. We work with a simplified implementation of the second-order (in the response field) approximation proposed in a previous work [Phys. Rev. E 84, 061150 (2011) and 86, 019904(E) (2012)], which greatly simplifies the frequency sector of the NPRG flow equations, while keeping a nontrivial frequency dependence for the two-point functions. The one-dimensional scaling function obtained within this approach compares very accurately with the scaling function obtained from the full second-order NPRG equations and with the exact scaling function. Furthermore, the approach is easily applicable to higher dimensions and we provide scaling functions and amplitude ratios in d = 2 and d = 3. We argue that our ansatz is reliable up to d similar or equal to 3.5.