Analytical study of the thermodynamic behavior of an antiferromagnetic Heisenberg model

By introducing a trial action S0, the thermodynamic properties of the two-dimensional (2D) and 3D quantum and classical antiferromagnetic Heisenberg model are studied and compared analytically with the variational cumulant expansion method. The free energy of the two models are expanded up to the fourth order and the critical temperature TN is given for each order and for different lattice structures. On the simple cubic lattice and square lattice, the sublattice magnetization Ms and the staggered susceptibility s are calculated.