New method for growing branched polymers and large percolation clusters belowpc

We propose a new Monte Carlo method for generating large branched polymers; it is based on enrichment of percolation clusters below $p_c$. We find that one must take care to distinguish two different ensemble averages: one at constant mass $s$ and the other at constant chemical distance $l$. For constant $s$, we obtain clusters belonging to the universality class of lattice animals, while for constant $l$ we get topologically one-dimensional structures for all $d$.