CALCULATION OF GENERALIZED WATSON SUMS WITH AN APPLICATION TO GENERALIZED HEISENBERG FERROMAGNET

A method of calculating the generalized Watson sums Φ(α,η)=k(eα[1-ηJ(k)J(0)]-1)-1 is presented. These sums over all reciprocal-lattice vectors in the first Brillouin zone are evaluated by approximating term with integrals which are then calculated analytically for 0≤α≤ and 0≤α≤1. To demonstrate the applicability of this technique, the magnetization of an anisotropic Heisenberg ferromagnet is calculated for the simple cubic (sc), bcc, and fcc lattices. © 1969 The American Physical Society.