Analysis and Discussion About How to Determine the Variatiotnal Parameters in the Variational-Cumulant Expansion

Four methods of determining the variational parameter in the varia tional-cumulant expansion (VCE) are studied on the 2-dimensional Ising model. A comparison with the exact result shows that the main-variation method is the best one at low temperature, the completevariational method is better than others at high temperature, the accumulation-point method is the best one to approximate the intermediate coupling region, and each of the methods is analyzed from the original formulas or conjectures. Some suggestions are given in order to get optimal results. The VCE is also analyzed Gom a point of view of symmetry breaking for the first time.