Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks

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Ziff, Robert M.
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Abstract
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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.
Comment: Small changes and figure update. Accepted for publication, PRL
Keywords
Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics
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