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}
}