Directed site lattice animals with restricted valence

The critical behaviour of directed site lattice animals having valence no larger than v is studied in the square lattice for the cases of v=2 and 3 by using exact enumerations. The authors also study the cases where the microscopic restrictions are anisotropic so that the universality hypothesis can be tested for the systems possessing a non-trivial preferred axis. As expected, for both the isotropic and anisotropic restrictions, series analysis together with some exact results show that when v=3 the systems have the same critical behaviour as the unrestricted case while for v=2 the systems belong to the same universality class as directed self-avoiding walks.