Site percolation on lattices with low average coordination numbers

  title={Site percolation on lattices with low average coordination numbers},
  author={Ted Yoo and Jonathan Tran and Shane Stahlheber and Carina E. Kaainoa and Kevin Djepang and Alex Small},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
We present a study of site and bond percolation on periodic lattices with (on average) fewer than three nearest neighbors per site. We have studied this issue in two contexts: by simulating oxides with a mixture of 2-coordinated and higher-coordinated sites and by mapping site-bond percolation results onto a site model with mixed coordination number. Our results show that a conjectured power-law relationship between coordination number and site percolation threshold holds approximately if the… 

Point to point continuum percolation in two dimensions

The outcome of the classic percolation approach is several power-law curves with some universal (critical) exponents. Here, the universality means that these power laws as well as their critical

Heat percolation in many-body flat-band localizing systems

Translationally invariant finetuned single-particle lattice Hamiltonians host flat bands only. Suitable short-range many-body interactions result in complete suppression of particle transport due to



Percolation thresholds on three-dimensional lattices with three nearest neighbors

We present a study of site and bond percolation on periodic lattices with three nearest neighbors per site. Essentially all previous studies of percolation in 3D have considered coordination numbers

Exact bond percolation thresholds in two dimensions

Recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices. Here we show how these results can be extended to other classes of graphs,

Simultaneous analysis of three-dimensional percolation models

We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice

Fast Monte Carlo algorithm for site or bond percolation.

  • M. NewmanR. Ziff
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
An efficient algorithm is described that can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system.

Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions

An exact method for determining the critical percolation probability, pc, for a number of two‐dimensional site and bond problems is described. For the site problem on the plane triangular lattice pc

Percolation on two- and three-dimensional lattices.

A highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff is applied to treat percolation problems to confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.

Universal formulas for percolation thresholds.

  • GalamMauger
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
A power law is postulated for both site and bond percolation thresh- olds and is found to be also valid for Ising critical temperatures.

Topology invariance in percolation thresholds

Abstract:An universal invariant for site and bond percolation thresholds (pcs and pcb respectively) is proposed. The invariant writes {pcs}1/as {pcb}‒1/ab = δ/d where as, ab and δ are positive

An Investigation of Site-Bond Percolation on Many Lattices

It is shown here that there are strong deviations from the known approximate equations in the line of threshold values, and an alternative parametrization is proposed that lies much closer to the numerical values.