Swelling of percolation clusters

The swelling of percolation clusters as models for gelling branched polymers is analyzed by using a simple mean-field approach (for all dimensions) and a Monte-Carlo simulation (for $d=3$, bond fluctuation method). The numerical swelling exponent $\mu '=0.443 \,\pm\, 0.008$ shows a significant deviation from the lattice animals solution $\mu '=0.5$, which is caused by the difference between quenched and annealed average procedures