2009
DOI: 10.1103/physrevlett.103.045701
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Abstract: The growth of two-dimensional lattice bond percolation clusters through a cooperative Achlioptas type of process, where the choice of which bond to occupy next depends upon the masses of the clusters it connects, is shown to go through an explosive, first-order kinetic phase transition with a sharp jump in the mass of the largest cluster as the number of bonds is increased. The critical behavior of this growth model is shown to be of a different universality class than standard percolation.

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Cited by 177 publications
(200 citation statements)
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“…[1] to describe a sudden appearance of a macroscopic cluster in a network growth model with the so-called product rule considered on the complete graph. This growth rule, named as the Achlioptas process (AP), is then studied on the two-dimensional lattice [2,3] and on the scalefree networks [4][5][6] as well, yielding similar results. That suddenness has been widely believed to indicate a discontinuity at the percolation transition in the thermodynamic limit [7,8], and the similar explosiveness has been observed with the other growth rules proposed later [9][10][11][12][13].…”
mentioning
confidence: 77%
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“…[1] to describe a sudden appearance of a macroscopic cluster in a network growth model with the so-called product rule considered on the complete graph. This growth rule, named as the Achlioptas process (AP), is then studied on the two-dimensional lattice [2,3] and on the scalefree networks [4][5][6] as well, yielding similar results. That suddenness has been widely believed to indicate a discontinuity at the percolation transition in the thermodynamic limit [7,8], and the similar explosiveness has been observed with the other growth rules proposed later [9][10][11][12][13].…”
mentioning
confidence: 77%
“…Sublinearity is estimated only by 6%, which may call for a huge system size like N ∼ 10 17 (beyond the present computing capability) to reach a reasonable scaling regime (g(t u ) 0.1) and get any sensible extrapolation to the thermodynamic limit. Most of previous studies [1][2][3][4][5][6][7][8][9][10][11][12][13]15] basically depend on the data in this supercritical regime (t > t c ). Nevertheless, the scaling plot with this natural cutoff shows a reasonable collapse including the dip structure at the end, but involving big statistical errors (not shown here).…”
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confidence: 99%
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“…These jumps are discontinuous phase transitions. However, when such mechanisms are mixed, even weakly, with mechanisms that merge components purely at random then the transitions vanish, or become at most weakly discontinuous characterized by very small power law exponents [30][31][32][33][34][35][36][37][38][39][40][41] , see Supplementary Methods and Supplementary Figs S1-S3.…”
Section: Discussionmentioning
confidence: 99%
“…This discontinuous percolation transition appears when the growth of the largest cluster is systematically suppressed thereby promoting the formation of several large components that eventually merge in an explosive way [40]. Several aggregation models, based on percolation, have been developed to achieve this change in the nature of transition [19,39,[41][42][43][44][45][46][47]. Recent numerical studies argue that the transition is really a continuous transition, with the discontinuity seen being due to the finite size of the lattice [48].…”
Section: Introductionmentioning
confidence: 99%