Bond Percolation on Random Lattices : Two and Three Dimensions

• Main Authors: Hsiao-Ping Hsu, 許曉萍
• Other Authors: Ming-Chang Huang
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/59427473262574494301

博士 === 中原大學 === 物理學系 === 87 === Random lattices provide a natural framework to study the effect on critical phenomena caused by randomness. We study percolation processes with uniform occupied probability on two-dimensional and three-dimensional random lattices. From the results of the percolating probability and the existence probability of the appearance of percolating clusters, we conclude that randomness enhances the occurrence of percolation. Then we determine the percolation threshold and critical exponents of the percolation transition. By studying the peaks and the standard deviations of the distribution function of the derivative of the existence probability of percolating cluster, we can obtain the percolation threshold and the critical exponent ν. By applying the finite-size scaling theory to the size of a percolating cluster and the mean cluster size distribution, we also estimate the critical exponents D and τ. Our results of these critical exponents strongly indicate that percolation model on random lattices belongs to the same universality class as the model defined on regular lattices. To go one step further than the universality, we examine the idea of universal scaling functions with non-universal metric factors, proposed by Fisher and Privman, in two dimensions. By adjusting three metric factors, we find that the percolating probability and the existence probability of the appearance of percolating clusters have the same scaling functions for square lattices and planar random lattices.