  We derive a set of equations expressing the parameters of the magnetic
interactions characterizing a strongly correlated electronic system in terms of
single-electron Green's functions and self-energies. This allows to establish a
mapping between the initial electronic system and a spin model including up to
quadratic interactions between the effective spins, with a general interaction
(exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii-Moriya
interaction and other symmetric terms such as dipole-dipole interaction. We
present the formulas in a format that can be used for computations via
Dynamical Mean Field Theory algorithms.
