  A new method to analytically determine the partition function zeroes of
weakly coupled theories on finite-size lattices is developed. Applied to the
lattice Schwinger model, this reveals the possible absence of a phase
transition at fixed weak coupling. We show how finite-size scaling techniques
on small or moderate lattice sizes may mimic the presence of a spurious phase
transition. Application of our method to the Gross-Neveu model yields a phase
diagram consistent with that coming from a saddle point analysis.
