Investigation of Variation of Cluster Size Distribution on Square Lattice for Various occupational Probabilities [ ]

This study investigated the variation in cluster sizes distribution on a square lattice using a Fortran program to populate square lattice haven specified the lattice size and corresponding occupational probability range. This program thereafter sorts the occupied lattice sites into good label using Hoshen and Kopelman algorithm. It then identifies all clusters present within the lattice, determine the cluster sizes distribution and group the cluster(s) according to size1, 2, 3, 4, 5, 10, 20, 30, 40, 50 and above respectively, With the entire procedure repeated for probability range starting from the initial (0.001) to the final (1.000) at a step size of 0.001 increments, tables and graphs results were then drawn, These results shows that the probability corresponding to the peak size distribution for all lattice studied increased toward threshold. Interestingly, the peak probability for size 50 and above for all studied cases suffered little absolute deviation relative to standard threshold value of 0.593 also the horizontal range of size distribution curve was noticed to reduce as size distribution increases, similarly an exponential relationship was noticed from the graph of horizontal range and corresponding size distribution for all studied cases which speculates that as x (size distribution) → ∞ that y (horizontal range) → 0 and vice versa.