EFFECTIVE MEAN-FIELD THEORY-BASED ON CUMULANT EXPANSION - A NEW APPROACH METHOD ORDER BY ORDER

We propose in this paper an effective mean-field theory, which makes the calculation for any observable being performed in a general form of cumulant expansion. The effective mean-field equation with reasonable physical annotation, which is obtained from the lower bound extreme value condition of free energy, can be applied to general statistic mechanics and Lagrangian quantum theory. By applying it to lattices, our theory, for various models containing nonuniform system and nonequilibrium phenomenon, can give a realistic scheme to study the nonperturbative effect order by order. As a testing example to two-dimensional sing model, we obtain a result approaching the Onsager solution order by order.