Abstract
A formulation for disordered Heisenberg spin systems and alloys by the coherent potential approach is rigorously developed to involve cluster effects and off-diagonal randomness. In the momentum representation the diagonal matrix elements of the averaged t-matrix are obtained in a Fourier-analysed form. Equations to determine the unknown Fourier coefficients of the coherent energy are given exactly by requiring that each Fourier coefficient of the t-matrix vanish. An approximating method based on the exact formulation is presented for linear chains in magnetic systems. This applies to general short-range potentials and always retain the translational symmetry.