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We consider a single magnetic impurity described by the spin--anisotropics-d(f) exchange (Kondo) model and formulate scaling equation for thespin-anisotropic model when the density of states (DOS) of electrons is a powerlaw function of energy (measured relative to the Fermi energy). We solve thisequation containing terms up to the second order in coupling constants in termsof elliptic functions. From the obtained solution we find the phasescorresponding to the infinite isotropic antiferromagnetic Heisenberg exchange,to the impurity spin decoupled from the electron environment (only for thepseudogap DOS), and to the infinite Ising exchange (only for the divergingDOS). We analyze the critical surfaces, corresponding to the finite isotropicantiferromagnetic Heisenberg exchange for the pseudogap DOS.

Spin-anisotropic magnetic impurity in a Fermi gas: poor man's scaling equation integration