  In theories with spontaneous symmetry breaking, the loop expansion of the
effective potential is awkward. In such theories, the exact effective potential
$V(\phi_c,T)$ is real and convex (as a function of the classical field
$\phi_c$), but its perturbative series can be complex with a real part that is
concave. These flaws limit the utility of the effective potential, particularly
in studies of the early universe. A generalization of the effective potential
is available that is real, that has no obvious convexity problems, and that can
be computed in perturbation theory. For the theory with classical potential
$V(\phi) = (\lambda/4)(\phi^2 - \sigma^2)^2$, this more-effective potential
closely tracks the usual effective potential where the latter is real $|\phi_c|
\geq \sigma/\sqrt{3}$ and naturally extends it to $\phi_c = 0$, revealing that
the critical temperature at the one-loop level runs from $T_C \approx 1.81
\sigma$ for $\lambda = 0.1$ to $T_C \approx 1.74 \sigma$ for $\lambda = 1$.
