Self-consistent expansion results for the nonlocal Kardar-Parisi-Zhang equation

Predictions for the scaling exponents of the nonlocal Kardar-Parisi-Zhang (NKPZ) equations are discussed. Self-consistent expansion (SCE) method is used to derive reliable results that are consistent with the exact one-dimensional result. It is demonstrated that the results obtained using SCE recover an exact result for a subfamily of the NKPZ models in one dimension. It is shown that SCE result is the only one compatible with simple observations on the dependence of the dynamic exponent z in the NKPZ model on the exponent ρ characterizing the decay of the nonlinear interaction.