A LATTICE TEST OF ALTERNATIVE INTERPRETATIONS OF TRIVIALITY IN (LAMBDA-PHI(4))(4) THEORY

There are two physically different interpretations of ''triviality'' i n (lambda Phi(4))(4) theories. The conventional description predicts a second-order phase transition and that the Higgs mass m(h) must vanis h in the continuum limit if v, the physical vev is held fixed. An alte rnative interpretation, based on the effective potential obtained in ' 'triviality-compatible'' approximations (in which the shifted ''Higgs' ' field h(x) = Phi(x) - (Phi) is governed by an effective quadratic Ha miltonian) predicts a phase transition that is very weakly first-order and that mh and v are both finite, cutoff-independent quantities. To test these two alternatives, we have numerically computed the effectiv e potential on the lattice. Three different methods were used to deter mine the critical bare mass for the chosen bare coupling value. All gi ve excellent agreement with the literature value. Two different method s for obtaining the effective potential were used, as a control on the results. Our lattice data are fitted very well by the predictions of the unconventional picture, but poorly by the conventional picture.