Strong evidence supports the idea that pure φ 4 field theory is "trivial" or non-interacting. Should such a situation persist when gauge fields are present, it is fair to question the idea of symmetry breaking (and gauge boson mass generation) by elementary scalars. An alternative possibility, suggested by the consideration of toy models, is that a consistent non-trivial theory may exist for only a select range of parameters, implying for example that the standard model Higgs mass may be bounded or calculable. In principle the Monte Carlo renormalization group can be used to examine this possibility. Here the formalism is elucidated and the results of the first calculation for the standard model are presented.