  Previous studies of a simple four-fermion model with staggered fermions in 3D
have shown the existence of an exotic quantum critical point, where one may be
able to define a continuum limit of the Paramagnetic Strong Phase (or the PMS
phase). We believe the existence of the critical point suggests a new mechanism
for generating fermion masses. In this work we begin the search for this
quantum critical point in 4D by extending the 3D model to 4D. Unlike in 3D, now
we do find evidence for an intermediate spontaneously broken phase (FM phase)
and are able compute the phase boundaries accurately. In terms of the bare
coupling, the width of the intermediate region appears to be quite small.
