# Percolation thresholds, critical exponents, and scaling functions on planar random lattices and their duals.

@article{Hsu1999PercolationTC, title={Percolation thresholds, critical exponents, and scaling functions on planar random lattices and their duals.}, author={Hsiao-Ping Hsu and M. C. Huang}, journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics}, year={1999}, volume={60 6 Pt A}, pages={ 6361-70 } }

The bond-percolation process is studied on periodic planar random lattices and their duals. The thresholds and critical exponents of the percolation transition are determined. The scaling functions of the percolating probability, the existence probability of the appearance of percolating clusters, and the mean cluster size are also calculated. The simulation result of the percolation threshold is p(c)=0.3333+/-0.0001 for planar random lattices, and 0.6670+/-0.0001 for the duals of planar random…

## 25 Citations

### Percolation Thresholds, Critical Exponents, And Scaling Functions On Spherical Random Lattices And Their Duals

- Mathematics
- 2002

Bond-percolation processes are studied for random lattices on the surface of a sphere, and for their duals. The estimated threshold is 0.3326 ± 0.0005 for spherical random lattices and 0.6680 ±…

### Percolation on a multifractal scale-free planar stochastic lattice and its universality class.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

The results suggest that the percolation on WPSL belong to a separate universality class than on all other planar lattices.

### Percolation thresholds on two-dimensional Voronoi networks and Delaunay triangulations.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

The results rule out the conjecture by Hsu and Huang that the bond thresholds are 2/3 and 1/3, respectively, but support the conjecture of Wierman that, for fully triangulated lattices other than the regular triangular lattice, the bond threshold is less than 2 sin pi/18 approximately 0.3473.

### Scaling and localization in fracture of disordered central-force spring lattices: Comparison with random damage percolation

- Physics
- 2006

We analyze statistical and scaling properties of the fracture of two-dimensional (2D) central-force spring lattices with strong disorder by means of computer simulation. We run fracture simulations…

### Percolation thresholds on planar Euclidean relative-neighborhood graphs.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

The asymptotic degree and diameter of RNGs are determined and estimated and the common percolation critical exponents from the RNG data are deduced to verify that the associated universality class is that of standard 2D percolations.

### Contact process on weighted planar stochastic lattice

- Computer ScienceJournal of Statistical Mechanics: Theory and Experiment
- 2022

The critical behavior of the disordered system using extensive simulations shows the critical behavior is distinct from that on a regular lattice, suggesting it belongs to a different universality class.

### Scaling, localization and anisotropy in fracturing central-force spring lattices with strong disorder

- Physics
- 2006

We analyze scaling and localization phenomena in the fracture of a random central-force spring lattice model with strong disorder by means of computer simulation. We investigate the statistical and…

### Structural properties of scale‐free networks

- Computer Science
- 2005

The structural properties of scale-free networks are studied and it is shown that in the regime 2 < < 3 the networks are resilient to random breakdown and the percolation transition occurs only in the limit of extreme dilution.

### Effect of disorder strength on the fracture pattern in heterogeneous networks

- Materials Science
- 2007

We present simulation results on fracture and random damage percolation in disordered two-dimensional (2D) lattices of different sizes. We systematically study the effect of disorder strength on the…

### Universality class of explosive percolation in Barabási-Albert networks

- Materials ScienceScientific Reports
- 2019

This work study explosive percolation in Barabási-Albert network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process finds that the critical exponents ν, α, β and γ for m > 1 are found to be independent not only of the value of m but also of PR and SR.

## References

SHOWING 1-3 OF 3 REFERENCES

### 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…

### Statistical Field Theory

- Physics
- 1989

Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a…