Self-Avoiding Walks of Continuous Spatial Dimensionality

The possibility of describing the continuous variation ${\ensuremath{\nu}}_{D}$ with $D$, where ${\ensuremath{\nu}}_{D}$ 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 ${\ensuremath{\nu}}_{d}$ of such accelerated self-avoiding walks is studied with the help of computer simulation. The results indicate that ${\ensuremath{\nu}}_{d}$ reproduces ${\ensuremath{\nu}}_{D}$.