Finite Size Scaling in Three-Dimensional Bootstrap Percolation

Finite Size Scaling in Three-Dimensional Bootstrap Percolation

Finite size scaling in three-dimensional bootstrap percolation

We consider the problem of bootstrap percolation on a three dimensional lattice and we study its finite size scaling behavior. Bootstrap percolation is an example of Cellular Automata defined on the d-dimensional lattice {1, 2, ..., L} in which each site can be empty or occupied by a single particle; in the starting configuration each site is occupied with probability p, occupied sites remain o...

Finite-Size Scaling in Percolation

This work is a detailed study of the phase transition in percolation, in particular of the question of finite-size scaling: Namely, how does the critical transition behavior emerge from the behavior of large, finite systems? Our results rigorously locate the proper window in which to do critical computation and establish features of the phase transition. This work is a finite-dimensional analog...

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...

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...