Self-avoiding walks in four dimensions: Logarithmic corrections to scaling

Monte Carlo techniques are used to study the conformational properties of self-avoiding walks on the four-dimensional cubic lattice. Both the mean-square end-to-end distance and radius of gyration are found to diverge as $N{\left(\ln N\right)}^q$, where $N$ is the number of steps in the walk. The results suggest a value $q\approx 0.31$, whereas the renormalization-group prediction is $q=0.375\mathrm{}$; this small discrepancy is attributable to slowly decaying correction terms.