Comparison of perturbative RG theory with lattice data for the 4d Ising model

Predictions for (ϕ4)4 theory from renormalization-group-improved perturbation theory, as formulated by Lüscher and Weisz, are compared to published (and some unpublished) data from lattice Monte Carlo simulations of the 4-dimensional Ising model.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 ZˆR 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.