Scaling of self-avoiding walks and self-avoiding trails in three dimensions

Scaling of Self-Avoiding Walks and Self-Avoiding Trails in Three Dimensions

Scaling of Self-Avoiding Walks and Self-Avoiding Trails in Three Dimensions

Motivated by recent claims of a proof that the length scale exponent for the end-to-end distance scaling of self-avoiding walks is precisely 7/12 = 0.5833 . . ., we present results of large-scale simulations of self-avoiding walks and self-avoiding trails with repulsive contact interactions on the hypercubic lattice. We find no evidence to support this claim; our estimate ν = 0.5874(2) is in ac...

Scaling of self-avoiding walks in high dimensions

We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte Carlo simulations up to length N = 16 384, 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...

Self-avoiding walks, neighbour-avoiding walks and trails on semiregular lattices

We study self-avoiding and neighbour-avoiding walks and lattice trails on two semiregular lattices, the (3.122) lattice and the (4.82) lattice. For the (3.122) lattice we find the exact connective constant for both self-avoiding walks, neighbour-avoiding walks and trails. For the (4.82) lattice we generate long series which permit the accurate estimation of the connective constant for self-avoi...

Self-avoiding walks and trails on the 3.122 lattice

We find the generating function of self-avoiding walks (SAWs) and trails on a semi-regular lattice called the 3.122 lattice in terms of the generating functions of simple graphs, such as SAWs, self-avoiding polygons and tadpole graphs on the hexagonal lattice. Since the growth constant for these graphs is known on the hexagonal lattice we can find the growth constant for both walks and trails o...