Test of scaling exponents for percolation-cluster perimeters

The formula for the fractal dimensionality of the perimeter (hull) of a percolation cluster, df'=1+1/{ν}, proposed recently by Sapoval, Rosso, and Gouyet, is shown to imply for the perimeter scaling exponents {τ}'=1+2{ν}/(1+{ν}), {σ}'=1/(1+{ν}), and {γ}'=2. Monte Carlo simulations of very large perimeter-generating walks yield {τ}'=2.143±{}0.002 and df'=1.751±{}0.002, consistent with these predictions (on the assumption that {ν}=(4/3)). The walks are also used to determine pc=0.5927 5±{}0.0000 3 for site percolation on a square lattice.