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 nc is a universal quantity, dependent upon the system shape but independent of the lattice and percolation type. Values of nc 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.