# Determination of the critical exponent β in site percolation using Average Occupation Probability on a square lattice

### Abstract

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 – p_{c} 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.

*Proceedings of the Samahang Pisika ng Pilipinas*

**29**, SPP2011-5A-3 (2011). URL: https://paperview.spp-online.org/proceedings/article/view/3139.