STUDY OF THE QUANTUM SPIN HEISENBERG-MODEL WITH VARIATIONAL-CUMULANT EXPANSION TO THE 3RD-ORDER

The quantum spin Heisenberg model is studied with the variational-cumu lant expansion (VCE) method. The free energy of the model is expanded to the third order. The internal energy and specific heat are calculat ed and displayed from the first to the third order. The critical tempe rature T(c) is given. One finds that the value of T(c) got in the firs t order of the VCE is equivalent with that of the mean-field theory an d the second order is equivalent with the first order of the 1/z expan sion. The third order gives a more accurate correction for various lat tices and spins.