The Study Of Explosive Percolation On Two-Dimensional Lattice

In this thesis, we mainly study the Explosive Percolation based on the Product Rule on twodimensional structures. The physical quantities of maximum cluster size, moments,susceptibility and wrapping probabilities are obtained. The threshold and exponents are foundprecisely. Finally we obtain the conclusion corresponded with the results which wasdemonstrated by Achlioptas et al, that is, the phase transition of Explosive Percolation isdiscontinuous.In part1, we present the background of classic percolation and some basic conceptions. Thecommonly used algorithms are also introduced. And then, we bring in the conception ofExplosive Percolation and make a brief introduction of its development status.In part2, we demonstrate the Random Growth model and the new cluster evolution rulecalled Product Rule. Then we compare the threshold and exponents of Explosive Percolationwhich was originally studied by Achlioptas, D’Souza and Spencer with those of the classic ERmodel and BF model which was proposed by Bohman and Frieze.In part3, we carry on the numerical simulation of Explosive Percolation on the regular twodimensional lattices with unrestricted bond placement that the bond can be placed not onlybetween different clusters but also within the same cluster proposed by Raddicchi and Fortunatoaccording to the scaling behavior of Explosive Percolation on the square lattice studied by Ziff.At the same time, we also analyze the scaling behavior of Explosive Percolation on two types oflattice.