Superscaling of Percolation on Rectangular Domains

For percolation on (RL)×L two-dimensional rectangular domains with a width L and aspect ratio R, we propose that the existence probability of the percolating cluster Eₚ(L,ε,R) as a function of L, R, and deviation from the critical point ε can be expressed as F(εL^yₜRᵃ), where yₜ≡1/ν is the thermal scaling power, a is a new exponent, and F is a scaling function. We use Monte Carlo simulation of bond percolation on square lattices to test our proposal and find that it is well satisfied with $a=0.14(1)$ for $R>2$. We also propose superscaling for other critical quantities.