PERCOLATION AND FINITE SIZE SCALING IN SEVEN DIMENSIONS

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...

Corrections to Finite Size Scaling in Percolation

A 1/L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18, 22, . . . 1594 is considered. Certain spanning probabilities were determined by Monte Carlo simulations, as continuous functions of the site occupation probability p. We estimate the critical threshold pc by applying the quoted expansion to these data. A...

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

Finite-size scaling of energylike quantities in percolation.

We study the bond-percolation model in two and three dimensions by Monte Carlo simulation, and investigate the finite-size scaling behavior of several quantities that account for fluctuations of the total numbers of clusters and occupied bonds, Nc and Nb, respectively. These quantities include C(2c) = ( - 2)/Ld and C(cb) = ( - )/Ld, where L is the linear system size and...

Finite Size Scaling in Three-Dimensional Bootstrap Percolation