Large logarithmic rescaling of the scalar condensate: new lattice evidences

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'.