Interpolating lagrangians and U(1) gauge theory on the lattice

We apply the idea of a linear interpolating expansion to compact U(1) on the lattice, setting up an action Sδ which at δ=1 reproduces the standard gauge-invariant action but at δ=0 has the form of its weak-coupling limit times an arbitrary parameter β'. We then evaluate the plaquette energy EP through O(δ3), fixing β' by the requirement that dEP/dβ'=0. Approaching the critical point βc from above, we are able to reproduce closely the Monte Carlo results down to a value of β at which the stationary point in β' disappears. This value is progressively nearer to βc in higher orders of the δ expansion. (orig.)