  This paper is a contribution to a program to see symmetry breaking in a
weakly interacting many Boson system on a three dimensional lattice at low
temperature. It is part of an analysis of the "small field" approximation to
the "parabolic flow" which exhibits the formation of a "Mexican hat" potential
well. Here we prove the existence of and bounds on the background and critical
fields that arise from the steepest descent attack that is at the core of our
renormalization group step anaylsis of these models.
