Finite-Size Scaling in Percolation

THE SCALING LAW FOR THE DISCRETE KINETIC GROWTH PERCOLATION MODEL

The Scaling Law for the Discrete Kinetic Growth Percolation Model The critical exponent of the total number of finite clusters α is calculated directly without using scaling hypothesis both below and above the percolation threshold pc based on a kinetic growth percolation model in two and three dimensions. Simultaneously, we can calculate other critical exponents β and γ, and show that the scal...

Finite-size scaling analysis of percolation in three-dimensional correlated binary Markov chain random fields.

Percolation and finite-size scaling properties in three-dimensional binary correlated Markov-chain random fields on a cubic lattice are computed by extensive Monte Carlo simulation. At short correlation scales, the percolation threshold in correlated random fields decreases as the correlation scale increases. The rate of decrease rapidly diminishes for correlation lengths larger than 2-3 lattic...

Finite-Size Scaling in Two-dimensional Continuum Percolation Models

We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation data in the 2D continuum models obey the same scaling expression of massM to sample size L as generally accepted for isotropic lattice problems, but with a p...

Critical percolation in high dimensions: critical exponents, finite size scaling and random walks

Polydispersity Effect and Universality of Finite-Size Scaling Function

We derive an equation for the existence probability Ep for general percolation problem using an analytical argument based on exponential-decay behaviour of spatial correlation function. It is shown that the finite-size scaling function is well approximated by the error function. The present argument explain why it is universal. We use Monte Carlo simulation to calculate Ep for polydisperse cont...

The Birth of the Infinite Cluster: Finite-size Scaling in Percolation

We address the question of finite-size scaling in percolation by studying bond percolation in a finite box of side length n, both in two and in higher dimensions. In dimension d = 2, we obtain a complete characterization of finite-size scaling. In dimensions d > 2, we establish the same results under a set of hypotheses related to so-called scaling and hyperscaling postulates which are widely b...