title: Dimensional dependence of phase transitions in explosive percolation.
abstract: To understand the dependence of phase-transition natures in explosive percolations on space dimensions, the number n(cut) of cutting bonds (sites) and the fractal dimension d(CSC) of the critical spanning cluster (CSC) for the six different models introduced in Phys. Rev. E 86, 051126 (2012) are studied on two- and three-dimensional lattices. It is found that n(cut)(L→∞)=1 for the intrabond-enhanced models and the site models on the two-dimensional square lattice with lattice size L. In contrast, n(cut) for the intrabond-suppressed models scales as n(cut)≃L(d(cut)) with d(cut)=1. d(CSC)=2.00(1) is obtained for the intrabond-enhanced models and the site models, while d(CSC)=1.96(1)(<2) is obtained for the intrabond-suppressed models in two dimensions (2D). These results strongly support that the intrabond-enhanced models and the site models undergo the discontinuous transition in 2D, while the intrabond-suppressed models do the continuous transition in 2D. On the three-dimensional cubic lattice, we find that d(cut)>0 and d(CSC)=2.8(1)(<3) for all six models, which indicates that the models undergo the continuous transition. Based on the finite-size scaling analyses of mean cluster size and order parameter, all six models in 3D show nearly the same critical phenomena within numerical errors.
authors.affiliation: Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
authors.forename: Woosik
authors.initials: W
authors.lastname: Choi
authors.affiliation: Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
authors.forename: Huiseung
authors.initials: H
authors.lastname: Chae
authors.affiliation: Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
authors.forename: Soon-Hyung
authors.initials: SH
authors.lastname: Yook
authors.affiliation: Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
authors.forename: Yup
authors.initials: Y
authors.lastname: Kim
mesh_terms: D017709:Fractals; D008962:Models, Theoretical; D044367:Phase Transition