Scaling of self-avoiding walks in high dimensions

Abstract

We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte Carlo simulations up to length N = 16384, providing the first such results in dimensions d > 4 on which we concentrate our analysis. We analyse the scaling behaviour of the partition function and the statistics of nearest-neighbour contacts, as well as the average geometric size of the walks, and compare our results to l/d-expansions and to excellent rigorous bounds that exist. In particular, we obtain precise values for the connective constants, μ5 = 8.838 544(3), μ6 = 10.878 094(4), μ7 = 12.902 817(3), μ8 = 14.919 257(2) and give a revised estimate of μ4 = 6.774 043(5). All of these are by at least one order of ..