Cumulant Expansion in Intermediate Coupling Region in U(l) Lattice Gauge Theory

Determining the parameters in the i-th order approximation in the cumulant expansion from the requirement that the correction to the zeroth order approximation is zero or the smallest, we show in the example of calculating the Polyakov line < L > of U(1) gauge model at finite temperature with N_T = 1-to 5-th order that the expansion works well not only in the strong and weak coupling regions, but also in the intermediate coupling region except the very vicinity of the phase transition point. The calculated < L > is in agreement with Monte Carlo simulations.