Self-consistent expansion for the Kardar-Parisi-Zhang equation with correlated noise

A minor modification of the self-consistent expansion (SCE) for the Kardar-Parisi-Zhang (KPZ) system with uncorrelated noise is used to obtain the exponents in systems where the noise has spatial long-range correlations. For d-dimensional systems with correlations of the form D((r) over right arrow-(r) over right arrow', t-t') = 2D(0)\(r) over right arrow-(r) over right arrow'\(2 rho-d)delta(t-t'), (rho > 0), we find a lower critical dimension d(0)(rho) = 2 + 2 rho, above which a perturbative Edwards-Wilkinson (EW) solution appears. Below the lower critical dimension two solutions exist, each in a different, distinct region of rho. For small rho's the solution of KPZ with uncorrelated noise is recovered. For large rho's a rho-dependent solution is found. The existence of only one solution in each region of rho is not a result of a competition between two solutions but a direct outcome of the SCE equation.