Universality of Finite-Size Corrections to the Number of Critical Percolation Clusters

Monte Carlo simulations on a variety of finite 2D percolating systems at criticality suggest that the excess number of clusters over the bulk value $n_c$ is a universal quantity, dependent upon the system shape but independent of the lattice and percolation type. Values of $n_c$ are found to high accuracy, and for bond percolation are in accord with the theoretical predictions of Temperley and Lieb [Proc. R. Soc. London A 322, 251 (1971)], and Baxter, Temperley, and Ashley [Proc. R. Soc. London A 358, 535 (1978)], whose results we have evaluated explicitly in terms of simple algebraic numbers. Fluctuations are also studied.