SEARCHING FOR REGULARITIES IN THE SQUARE NET SITE PERCOLATION - Montenegro Joo, Javier (2005)
A statistical study of nearest neighbors site percolation in 75x75, 150xl50 and 225x225 square lattices has been performed with the aim on finding out possible regularities; to accomplish this, a percolation Monte Cario simulation software was specially developed and statistics from 100 completed percolations in each lattice were obtained. The investigation was carried-out on the threshold ofpercolation, this is, setting the probability in the critica! value P = Pe = 0.5928 throughout all the simulations. It is important to notice the fact that in order to achieve the 100 successful percolations required for the statistics, it was necessary to execute the simulations many more times, because very many of them resulted frustrated, not attaining percolation. Another important observation is the fact that percolation was not always achieved by the largest clusters, there were instances where the percolating clusters were unsuspected thin clusters far from being the fattest ones. Regularities have been observed in the number of resulting clusters and in the number of step necessary to achieve percolation. lt is concluded that additional research with much larger lattices would help to wipe away sorne subsisting doubts.