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

TL;DR

This paper compares perturbative renormalization-group predictions with lattice Monte Carlo data for the 4d Ising model, finding good overall agreement but notable discrepancies in wavefunction renormalization and propagator behavior near the phase transition.

Contribution

It provides a detailed comparison between RG-improved perturbation theory and lattice data for the 4d Ising model, highlighting areas of agreement and discrepancy.

Findings

Good agreement in most predictions

Significant deviation in wavefunction-renormalization constant Z_R

Propagator deviations increase near the continuum limit

Abstract

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perturbation theory, as formulated by Luescher and Weisz, are compared to published (and some unpublished) data from lattice Monte-Carlo simulations of the 4-dimensional Ising model.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