The Phase Structure of the Weakly Coupled Lattice Schwinger Model

We develop a new expression for the partition function of the weakly coupled lattice Schwinger model with Wilson fermions from which its Lee--Yang zeroes are easily determined. Finite--size scaling then recovers previous numerical results for the small and moderate lattice sizes to which those studies were confined. On large lattices, however, the zeroes fail to accumulate on the hopping parameter axis, the consequence of which is the absence of a zero fermion mass phase transition in the Schwinger model with single flavour Wilson fermions at constant weak gauge coupling.