The growth constant of uniform star polymers in a slab geometry

The authors consider uniform star-branched polymer molecules, modelled by the corresponding graph weakly embedded in a simple cubic lattice, confined to a parallel-sided slab. In three (and higher) dimensions they show that the limiting entropy per bond is independent of the number of branches in the star and is equal to the connective constant of a self-avoiding walk on that subset of the lattice. In two dimensions, however, the limiting entropy per bond of a three-branch star is shown to be strictly less than that for a self-avoiding walk and present numerical evidence that this is a general result in two dimensions.