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.

25 pages, uuencoded compressed (using GNU's gzip) tar file containing 1 LaTeX2e file + 1 encapsulated Postscript figure + elsart.cls + elsart.sty + elsart12.sty. A full Postscript version of this paper is available at http://www.ba.infn.it/disk$gruppo_4/cosmai/www/papers/204-95.PS