Universal finite-size scaling for percolation theory in high 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...

Finite-size scaling theory for explosive percolation transitions.

The finite-size scaling (FSS) theory for continuous phase transitions has been useful in determining the critical behavior from the size-dependent behaviors of thermodynamic quantities. When the phase transition is discontinuous, however, FSS approach has not been well established yet. Here, we develop a FSS theory for the explosive percolation transition arising in the Erdős and Rényi model un...

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

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...

Universal Finite-size-scaling Functions

The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniv...