Explosive percolation is continuous, but with unusual finite size behavior.

摘要: We study four Achlioptas-type processes with ``explosive'' percolation transitions. All transitions are clearly continuous, but their finite size scaling functions not entirely holomorphic. The distributions of the order parameter, i.e., relative ${s}_{\mathrm{max}}/N$ largest cluster, double humped. But---in contrast to first-order phase transitions---the distance between two peaks decreases system $N$ as ${N}^{\ensuremath{-}\ensuremath{\eta}}$ $\ensuremath{\eta}g0$. find different positive values $\ensuremath{\beta}$ (defined via $⟨{s}_{\mathrm{max}}/N⟩\ensuremath{\sim}(p\ensuremath{-}{p}_{c}{)}^{\ensuremath{\beta}}$ for infinite systems) each model, showing that they all in universality classes. In contrast, exponent $\ensuremath{\Theta}$ such observables homogeneous $(p\ensuremath{-}{p}_{c}){N}^{\ensuremath{\Theta}}$) is close to---or even equal to---$1/2$ models.