Universal amplitude ratio Gamma-/Gamma+ for two-dimensional percolation.

@article{Jensen2006UniversalAR,
  title={Universal amplitude ratio Gamma-/Gamma+ for two-dimensional percolation.},
  author={Iwan Jensen and Robert M. Ziff},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2006},
  volume={74 2 Pt 1},
  pages={
          020101
        }
}
  • I. Jensen, R. Ziff
  • Published 6 July 2006
  • Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
The amplitude ratio of the susceptibility (or second size moment) for two-dimensional percolation is calculated by two series methods and also by Monte Carlo simulation. The first series method is an approach based upon integrating approximations to the scaling function. The second series method directly uses low- and high-density series expansions of the susceptibility, going to unprecedented orders for both bond and site percolation on the square lattice. Putting all methods together we find… 
View on PubMed
arxiv.org
10 Citations
Background Citations
2

10 Citations

Citation Type

Citation Type

Results for a critical threshold, the correction-to-scaling exponent and susceptibility amplitude ratio for 2d percolation
FAST TRACK COMMUNICATION: Universal amplitude ratios of two-dimensional percolation from field theory
We complete the determination of the universal amplitude ratios of two-dimensional percolation within the two-kink approximation of the form factor approach. For the cluster size ratio, which has for…
High-temperature series expansions for the q-state Potts model on a hypercubic lattice and critical properties of percolation.
  • M. Hellmund, W. Janke
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2006
TLDR
The high-temperature series expansions of the susceptibility and free energy of the q-state Potts model on a D-dimensional hypercubic lattice ZD for arbitrary values of q are presented and the percolation threshold pc and critical exponent gamma are estimated.
Bond percolation for homogeneous two-dimensional lattices
Amplitude ratios for critical systems in the c=-2 universality class.
TLDR
A set of universal amplitude ratios for amplitudes in finite-size correction terms of critical systems in the universality class with central charge c=-2 is presented.
Monte Carlo simulation of the critical behavior near the percolation threshold with invaded cluster algorithm
TLDR
The critical behavior of the disordered three-dimensional Ising model with an impurity concentration close to the threshold of impurity percolation is investigated on high-performance computing systems.
Finite-size corrections for logarithmic representations in critical dense polymers
Fields, particles and universality in two dimensions
Percolation Lattices, Efficient Simulation of Large
  • R. Ziff
  • Computer Science, Physics
    Encyclopedia of Complexity and Systems Science
  • 2009
Discontinuous percolation transitions and lattice models of fractal boundaries and paths

References

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…