  Predictions for (phi^4)_4 theory from renormalization-group-improved
perturbation theory, as formulated by Luescher and Weisz, are compared to
published (and some unpublished) data from lattice Monte-Carlo simulations of
the 4-dimensional Ising model. Good agreement is found in all but one
respect:-- the change in the wavefunction-renormalization constant Z_R across
the phase transition is significantly greater than predicted. A related
observation is that propagator data in the broken phase show deviations from
free-propagator form -- deviations that become larger, not smaller, closer to
the continuum limit. More data closer to the critical point are needed to
clarify the situation.
