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An efficient method to compute magnetic exchange interactions in systems withstrong correlations is introduced. It is based on a magnetic force theoremwhich evaluates linear response due to rotations of magnetic moments and uses anovel spectral density functional framework combining our exact diagonalizationbased dynamical mean field and local density functional theories. Applicationsto spin waves and magnetic transition temperatures of 3d metal mono--oxides aswell as high--T_{c} superconductors are in good agreement with experiment

Calculation of Magnetic Exchange Interactions in Mott-Hubbard Systems