Excluded volume effects for branched polymers: Monte Carlo results

As a simple model of randomly branched polymers, we consider the different ways that N-bond trees may be self-avoidingly embedded on a lattice. A general Monte Carlo approach is developed and applied. The mean square radii of gyration of the conformations with a given N are found to vary with N as Nν, where ν?1.23 and ν?0.92 in two and three dimensions. The critical importance of volume exclusion for branched structures is discussed.