Corrections to scaling and phenomenological renormalization for 2-dimensional percolation and lattice animal problems
@article{Derrida1985CorrectionsTS, 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}, year={1985}, volume={46}, pages={1623-1630} }
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…
39 Citations
COMMENT: Phenomenological renormalisation of Monte Carlo data for percolation
- Physics
- 1985
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…
On surface properties of two-dimensional percolation clusters
- Physics
- 1995
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
- Physics
- 1991
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
- Physics
- 1988
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
- Mathematics
- 1987
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
- Mathematics
- 1990
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
- Physics
- 1986
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
- Physics
- 1990
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…
Dynamic structure factor of Heisenberg bilayer dimer phases in the presence of quenched disorder and frustration
- Physics
- 2020
We investigate the influence of quenched disorder on the dynamic structure factor of Heisenberg bilayers on the square, triangular, and kagome lattice in the quantum paramagnetic phase. Perturbative…
References
SHOWING 1-6 OF 6 REFERENCES
A combination of Monte Carlo and transfer matrix methods to study 2D and 3D percolation
- Physics
- 1985
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)
- Physics
- 1982
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
- Physics
- 1985
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