Corrected finite-size scaling in percolation

This Rapid Communication proposes a comprehensive scaling theory for percolation, which clarifies the intrinsic nature of finite-size scaling and effectively addresses the finite-size effects. This theory applies to extensive systems, including especially the explosive percolation. It is suggested that explosive percolation shares the same scaling law as normal percolation, but may suffer from more severe finite-size effects. Remarkably, in contrast to previous studies, relying on the framework of our theory, the present Rapid Communication suggests that for all systems, the universal scaling functions do not depend on the boundary conditions.