Fermions and the Gaussian effective potential

The effect of fermions on the Gaussian effective potential is studied in a variety of fermion-scalar models in 2, 3, and 4 dimensions. Both g{φ}{ψ}{}{ψ} and gφ²{ψ}{}{ψ} couplings are considered. Stability requires the bare g to be infinitesimal; gB{}²$=${G}²$/${I}₀$ with ${I}₀$ a divergent integral. This contrasts with large-N studies in which ${g}B$ remains finite. The presence of fermions encourages spontaneous symmetry breaking, and in 3+1 dimensions the fermions destabilize the already ``precarious'' ${{φ}}⁴$ theory.