Comparison of Perturbative RG Theory with Lattice Data for the 4d Ising Model

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perturbation theory, as formulated by Lüscher and Weisz, are compared to published (and some unpublished) data from lattice Monte-Carlo simulations of the 4-dimensional Ising model.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