Indirect RKKY interaction in any dimensionality

We present an analytical method which enables one to find the exact spatial dependence of the indirect RKKY interaction between the localized moments via the conduction electrons for the arbitrary dimensionality n. The corresponding momentum dependence of the Lindhard function is exactly found for any n as well. Demonstrating the capability of the method we find the RKKY interaction in a system of metallic layers weakly hybridized to each other. Along with usual ${2\mathrm{k}}_{\mathrm{F}}$ in-plane oscillations, the RKKY interaction has the sign-reversal character in a direction perpendicular to layers, thus favoring the antiferromagnetic type of layers' stacking.