The non-trivial phase of φ4-theory in a renormalisation group invariant approach

Massless φ4-theory is investigated in zero and four space-time dimensions. Path-integral linearisation of the φ4-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.