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 gφψ¯ψ and g${\phi }^2$ψ¯ψ couplings are considered. Stability requires the bare g to be infinitesimal; $g_B$ ${\mathrm{}}^2$=$G^2$/$I_0$ 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’’ ${\phi }^4$ theory.