Iterated fully coordinated percolation on a square lattice

Abstract

We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also occupied. Repeating this site selection process again yields the iterated fully coordinated percolation model. Our results show a substantial enhancement in the size of highly connected regions after each iteration (from ordinary to fully coordinated and then to iterated fully coordinated percolation). However, using Monte Carlo methods to determine the static critical exponents and normal mode analyses to determine the dynamic critical exponents, our results indicate that the ordinary, fully coordinated, and iterated fully coordinated percolation models belong to the same universality class. This is in contrast to our previous results [*] wherein a different universality class dynamically (but not statically) for fully coordinated percolation was indicated, though the differences in the dynamic exponents were small. A possible cause might be the different methods of generating clusters, i.e., in this work clusters were generated statically in square lattices while in our previous work clusters were grown dynamically, for studying the dynamic critical exponents. * E. Cuansing, J. H. Kim and H. Nakanishi, Phys. Rev. E, 60, 3670 (1999).