  We analyze the Schwinger model on an infinite lattice using the continuum
definition of the fermion determinant and a linear interpolation of the lattice
gauge fields. The possible class of interpolations for the gauge fields,
compatible with gauge invariance is discussed. The effective action for the
lattice gauge field is computed for the Wilson formulation as well as for
non-compact lattice gauge fields. For the non-compact formulation we prove that
the model has a critical point with diverging correlation length at zero gauge
coupling e. We compute the chiral condensate for e > 0 and compare the result
to the N-flavor continuum Schwinger model. This indicates that there is only
one flavor of fermions with the same chiral properties as in the continuum
model, already before the continuum limit is performed. We discuss how
operators have to be renormalized in the continuum limit to obtain the
continuum Schwinger model.
