Determination of the critical exponent β in site percolation using average occupation probability on a square lattice


Using the Average Occupation Probability in site percolation, the critical exponent β for a lattice (L × L) is determined. The results for different lattice sizes show that as the lattice becomes larger, the calculated β agrees better with that obtained from 2D scaling theory. There appears a common range of p-pc which can be used for any L to compute for β. We estimate that a minimum lattice size of 200 × 200 is necessary for the procedure to yield an acceptable value of the critical exponent.