  We present a precise lattice computation of the slope of the effective
potential for massless $(\lambda\Phi^4)_4$ 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
$(\lambda\Phi^4)_4$ 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
$h(x)=\Phi(x)-\langle\Phi\rangle$, 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.
