@inproceedings {capili-spp-2013, title = {Determination of the percolation critical exponent as measure of dimension}, booktitle = {Proceedings of the 31st Samahang Pisika ng Pilipinas Physics Congress}, year = {2013}, month = {23{\textendash}25 Oct 2013}, pages = {SPP2013-4C-6}, address = {University of San Carlos, Cebu City}, abstract = {
The critical exponent\ β\ related to the percolation probability describes the dimensionality of a specific lattice topology. The\ accurate determination of\ β\ will aid in distinguishing different universality classes. This work describes the fine tuning of the\ Sigma method developed previously by the authors in obtaining\ β. The approach uses the log-log plot of the percolation\ probability versus the difference of the occupation probability and the percolation threshold. Considering a symmetric distribution of points about the midpoint of this plot yields the\ β\ with (1) the lowest standard deviation and (2) the\ appropriate asymptotic behavior for both one and two-dimensional lattices.
}, author = {Micielle N Capili and Ronald S. Banzon and Cristine Villagonzalo} } @inproceedings {245, title = {Percolation critical exponent of a constrained lattice}, booktitle = {Proceedings of the 30th Samahang Pisika ng Pilipinas Physics Congress}, year = {2012}, month = {22{\textendash}24 Oct 2012}, pages = {SPP-2012-004}, address = {De La Salle Health Sciences Institute, Dasmari{\~n}as, Cavite}, abstract = {
We implement the Average Occupation Probability method to treat site percolation on a square lattice with banned sites. It was found that the introduction of banned sites increases the value of the percolation probability while reducing the value of the critical exponent\ β. The deviation of\ β\ in site percolation of a constrained lattice from that of a regular system suggests that these\ lattice\ topologies belong to two different universality classes.
}, author = {Micielle N Capili and Cristine Villagonzalo and Ronald S. Banzon} } @inproceedings {248, title = {Determination of the critical exponent β in site percolation using average occupation probability on a square lattice}, booktitle = {Proceedings of the 29th Samahang Pisika ng Pilipinas National Physics Congress}, year = {2011}, month = {24{\textendash}26 Oct 2011}, pages = {SPP2011-5A-3}, address = {University of the Philippines Diliman, Quezon City}, abstract = {
Using the Average Occupation Probability in site percolation, the critical exponent\ β\ for a lattice (L {\texttimes} 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 {\texttimes} 200 is necessary for the\ procedure to yield an acceptable value of the critical exponent.
}, url = {https://paperview.spp-online.org/proceedings/article/view/3139}, author = {Micielle N Capili and Cristine Villagonzalo and Ronald S. Banzon} } @inproceedings {capili-spp-2007, title = {Calculation of the average occupation probability for spanning cluster formation in site percolation}, booktitle = {Proceedings of the 25th Samahang Pisika ng Pilipinas Physics Congress}, year = {2007}, month = {24{\textendash}26 Oct 2007}, pages = {SPP-2007-192}, address = {University of the Phlippines Los Ba{\~n}os, Laguna}, abstract = {
The average occupation probability for spanning cluster formation in square lattice using site percolation was calculated. Starting with an empty lattice, sites were generated using a pseudo-random number generator. A cluster labeling procedure was implemented for the detection of a spanning cluster. Our results show that the average occupation probability decreases linearly with inverse lattice edge length. The average occupation probability{\textquoteright}s extrapolated value of 0.608 as the lattice size approaches infinity is found to be a good estimate of the accepted value for the site percolation threshold in two dimensions equal to 0.598.
}, author = {Micielle N Capili and Cristine Villagonzalo and Ronald S. Banzon} }