  We present a detailed discussion of Spontaneous Symmetry Breaking (SSB) in
$(\lambda\Phi^4)_4$. In the usual approach, inspired by perturbation theory,
one predicts a second-order phase transition, the Higgs mass $m_h$, related to
the value of the renormalized 4-point coupling, gets smaller when increasing
the ultraviolet cutoff and this leads to the generally quoted upper bounds
$m_h<$700-900 GeV. On the other hand, by exploring the structure of the
effective potential in those approximation consistent with `triviality', where
the Higgs mass does not represent a measure of any observable interaction, SSB
does not require an ultraviolet cutoff, the phase transition is first-order,
such that the massless `Coleman-Weinberg' regime lies in the broken phase, and
one gets only $m_h<$3 TeV from vacuum stability. To separate out the two
alternatives, we present a precise lattice computation of the slope of the
effective potential in the region of bare parameters indicated by the
Luscher~\&~Weisz and Brahm's analysis of the critical line. Our lattice data
strongly support the latter description of SSB. Indeed, our data cannot be
reproduced in perturbation theory, and then they confirm the existence on the
lattice of a remarkable phase of $(\lambda\Phi^4)_4$ where SSB is generated
through ``dimensional transmutation'', and show no evidence for residual
self-interaction effects of the shifted ``Higgs'' field
$h(x)=\Phi(x)-\langle\Phi\rangle$, in agreement with ``triviality''.
