Size and shape of directed lattice animals

Abstract

Uses position-space renormalisation and exact enumeration methods to study configurational properties of directed lattice animals (clusters of directed bonds, in which the tail of a new bond must be added to the head of existing bonds). Exponents are found for the divergence of correlation lengths parallel and perpendicular to the preferred axis. In addition an exponent is found that characterises the singularity of the directed animal generating function and critical points are located.