Explosive Percolation is Continuous, but with Unusual Finite Size Behavior

We study four Achlioptas-type processes with ``explosive'' percolation transitions. All transitions are clearly continuous, but their finite size scaling functions are not entirely holomorphic. The distributions of the order parameter, i.e., the relative size smax/N of the largest cluster, are double humped. But---in contrast to first-order phase transitions---the distance between the two peaks decreases with system size N as N^-η with η>0. We find different positive values of β (defined via ⟨smax/N⟩~(p-pc)^β for infinite systems) for each model, showing that they are all in different universality classes. In contrast, the exponent Θ (defined such that observables are homogeneous functions of (p-pc)N^Θ) is close to---or even equal to---$1/2$ for all models.