ON AN ANALYTIC-EXPRESSION FOR THE ONE-MAGNON DISPERSION-RELATION IN A HEISENBERG-ANTIFERROMAGNET

Using the Dyson-equation approach to spin-spin correlation functions we derive self-consistent mean-field equations for the antiferromagnetic spin-(1/2) Heisenberg model. An analytic expression for the one-magnon dispersion valid in D = 1, 2, 3 is obtained. For the linear chain it gives the exact result omega(k) = (pi/2)\sin k\ known from the Bethe ansatz. For the square lattice the same procedure leads to omega(k) = 1.188 x 2 square-root 1 - ((cos k(x) + cos k(y))/2)2 in agreement with recent Monte Carlo results. Values for the simple cubic lattice in three dimensions are also given.