  The determination of the Landau free energy (the grand thermodynamic
potential) by a perturbation theory is advanced to arbitrary order for the
specific case of non-interacting fermionic systems perturbed by a one-particle
potential. Peculiar features of the formalism are highlighted, and its
applicability for bosons is indicated. The results are employed to develop a
more explicit approach describing exchange interactions between spins of
Anderson's magnetic impurities in metals, semiconductors, and insulators.
Within the fourth order our theory provides on the equal footing formulae for
the Ruderman-Kittel-Kasuya-Yosida, Bloembergen-Rowland, superexchange, and
two-electron exchange integrals at non-zero temperature.
