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 gives a completely consistent picture of the energetics of candidate vacuum states. Further systematic patterns of solutions are presented