Saddle point instability in models of chiral symmetry breaking

We examine the stability of models of chiral symmetry breaking based on truncated Schwinger-Dyson equations. We incorporate renormalization group improvement through a running coupling constant. We confirm in a specific model that all chiral symmetry breaking solutions correspond to saddle points of the effective potential functional. The instability can be traced to momentum scales in the range from intermediate to infrared. The region from intermediate to ultraviolet is a completely consistent picture of the energetics of candidate vacuum states. Further systematic patterns of solutions are presented