Corrections to scaling and phenomenological renormalization for 2-dimensional percolation and lattice animal problems

  title={Corrections to scaling and phenomenological renormalization for 2-dimensional percolation and lattice animal problems},
  author={Bernard Derrida and Dietrich Stauffer},
  journal={Journal De Physique},
We continue and improve the transfer matrix approach of Derrida and de Seze by incorporating in two different ways the leading corrections to the asymptotic behaviour for wide strips. We find for the site percolation threshold in the square lattice p c =0.59274±0.00010, for the radius exponent of lattice animals 0.64075±0.00015, and for the inverse growth factor or critical fugacity 0.246150±0.000010 in the square lattice and 0.192925±0.000010 in the triangular lattice. These results are… 

Figures and Tables from this paper

COMMENT: Phenomenological renormalisation of Monte Carlo data for percolation

The accuracy of a phenomenological renormalisation which is based on Monte Carlo data is tested by investigating site percolation in a simple cubic lattice. The method appears to be very accurate and

Critical exponents and corrections to scaling for bond trees in two dimensions

The author has analysed the newly obtained series of the radius of gyration Rn and the number of clusters Nn for n-bond trees (i.e. branch polymers without loops) on the square (n<or=14) and

On surface properties of two-dimensional percolation clusters

The two-dimensional site percolation problem is studied by transfer-matrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and

Cooperative diffusion of animals on the square lattice

The collective diffusion of N-particle lattice animals without vacancies and mass up to N=86 is investigated on the square lattice. Using the transfer matrix technique, a cluster fractal dimension

Resistivity exponent of two-dimensional lattice animals

We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) ∼ Lζ, is

Conformal invariance for polymers and percolation

The author studies some conformal variance properties of the polymer and percolation problems in two dimensions. By analysing the transfer matrix spectrum of these models at criticality, their series

Diffusion on two-dimensional percolation clusters with multifractal jump probabilities

By means of Monte Carlo simulations we studied the properties of diffusion limited recombination reactions (DLRR's) and random walks on two dimensional incipient percolation clusters with

The efficient determination of the percolation threshold by a frontier-generating walk in a gradient

The frontier in gradient percolation is generated directly by a type of self-avoiding random walk. The existence of the gradient permits one to generate an infinite walk on a computer of finite

Theory of branched polymers on fractal lattices

A phenomenological approach, which takes into account the basic geometry and the topology of fractal lattices and of branched polymers, is used to derive a new expression for the Flory exponent



A combination of Monte Carlo and transfer matrix methods to study 2D and 3D percolation

In this paper we develop a method which combines the transfer matrix and the Monte Carlo methods to study the problem of site percolation in 2 and 3 dimensions. We use this method to calculate the

Finite‐size scaling and phenomenological renormalization (invited)

Research in recent years has shown that combining finite‐size scaling theory with the transfer matrix technique yields a powerful tool for the investigation of critical behavior. In particular, the

Introduction To Percolation Theory

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in

Phase Transitions and Critical Phenomena edited by C

  • Domb and J. L. Lebowitz,
  • 1984

Phase Transitions and Critical Phe

  • 1984

Introduction to Percolation Theory (Taylor and Francis, London

  • 1985