  Using two different methods, we have determined the rescaling of the scalar
condensate $Z\equiv Z_\phi$ near the critical line of a 4D Ising model. Our
lattice data, in agreement with previous numerical indications, support the
behavior $Z_\phi\sim \ln ({\Lambda})$, $\Lambda$ being the ultraviolet cutoff.
This result is predicted in an alternative description of symmetry breaking
where there are no upper bounds on the Higgs boson mass from `triviality'.
