  A new method to determine the phase diagram of certain lattice fermionic
field theories in the weakly coupled regime is presented. This method involves
a new type of weak coupling expansion which is multiplicative rather than
additive in nature and allows perturbative calculation of partition function
zeroes. Application of the method to the single flavour Gross-Neveu model gives
a phase diagram consistent with the parity symmetry breaking scenario of Aoki
and provides new quantitative information on the width of the Aoki phase in the
weakly coupled sector.
