HIGH-ORDER EFFECTS IN ACTION-VARIATIONAL APPROACHES TO LATTICE GAUGE-THEORY

A recently developed action-variational approach so far has been applied to various cases up to fourth order. To obtain more reliable information about the underlying mechanisms and to check if the accuracy of high-statistics Monte Carlo simulations can be reached computations up to the next even order turn out to be necessary. This was prevented up to now by the occurrence of huge combinatorial factors. In the present work we develop means to circumvent this obstacle. In addition, the case of finite temperatures is also considered. Our results allow us to establish the general features of the approach in detail and to predict the behavior of still higher orders. With respect to practical applications it turns out that the sixth order gives worse results than the fourth order, or, more generally, that there is no longer an improvement beyond the fourth order. This behavior appears to be related to the asymptotic nature of the expansion and to the conversion into powers of 1/beta needed. Ultimately it reflects limitations in the possibilities of compensating the action by the trial action.