For percolation on $(RL)\times L$ two-dimensional rectangular domains with a width $L$ and aspect ratio $R$, we propose that the existence probability of the percolating cluster $E_p(L,\epsilon ,R)$ as a function of $L$, $R$, and deviation from the critical point $\epsilon$ can be expressed as $F(\epsilon L^{y_t}{R}^a)$, where $y_t\equiv 1/\nu$ 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.

• Received 21 June 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.190601