Lattice effective potential of massless $(λΦ^4)_4$: `triviality' and spontaneous symmetry breaking

Abstract

We present a precise lattice computation of the slope of the effective potential for massless $(λΦ^4)_4$ theory in the region of bare parameters indicated by the Brahm's analysis of lattice data. Our results confirm the existence on the lattice of a remarkable phase of $(λΦ^4)_4$ where Spontaneous Symmetry Breaking is generated through ``dimensional transmutation''. The resulting effective potential shows no evidence for residual self-interaction effects of the shifted `Higgs' field $h(x)=Φ(x)-\langleΦ\rangle$, as predicted by ``triviality'', and cannot be reproduced in perturbation theory. Accordingly the mass of the Higgs particle, by itself, does not represent a measure of any observable interaction.