The Critical Temperature of Quantum Spin Model Determined with Variational-Cumulant Expansion

The variational-cumulant expansion (VCE)methodis used to calculate the quantum XY model, for which the trial action S₀ does not commute with the action S, with arbitrary magnitude of spin on various one-, twe and three-dimensional lattices. The free energy of the model is expanded to the third order and the analytical formulae of critical temperature T_c are given for each order. To testify this method in a wider range, the Heisenberg model on different lattices is also calculated, which has more comparable results. Weighted fitting method of statistical mathematics is adopted to predict T_c of infinite order.