Self-Avoiding Walks of Continuous Spatial Dimensionality

Abstract

The possibility of describing the continuous variation ${\nu }_D$ with $D$, where ${\nu }_D$ is the shape exponent of self-avoiding walks and $D$ the spatial dimensionality, is investigated. A dimensionality $d$ is associated with the increase of a walk's volume with its length. The value of $d$ is varied at will through an extension (acceleration) of walks on all scales of length. The shape exponent ${\nu }_d$ of such accelerated self-avoiding walks is studied with the help of computer simulation. The results indicate that ${\nu }_d$ reproduces ${\nu }_D$.