  Massless $\phi^{4}$-theory is investigated in zero and four space-time
dimensions. Path-integral linearisation of the $\phi ^{4}$-interaction defines
an effective theory, which is investigated in a loop-expansion around the mean
field. In zero dimensions this expansion converges rapidly to the exact
potential obtained numerically. In four dimensions its lowest order (mean-field
approximation) produces a real and convex effective potential. Two phases are
found. In one the renormalisation group improved one-loop effective potential
is recovered as the leading contribution near the classical minimum. This
phase, however, is unstable. The second (precarious) phase is found to have
lower vacuum energy density. In this phase a dynamical mass is generated. The
results are renormalisation group invariant.
