Hausdorff dimension and fluctuations for the largest cluster at the two-dimensional percolation threshold

Stauffer, Dietrich

doi:10.1007/bf01325509

Cited by 24 publications

(10 citation statements)

References 9 publications

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“…As expected [16], these functions show a maximum around the "critical" value of Z bound . The agreement between experiment and theory is good, except for the highest values Z bound where the fluctuations should vanish for z = 79.…”

Section: Analysis Of Datasupporting

confidence: 81%

Analyzing fragmentation of simple fluids with percolation theory

et al. 2000

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Section: Analysis Of Datasupporting

confidence: 81%

Analyzing fragmentation of simple fluids with percolation theory

et al. 2000

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“…Thus, to compare values of R 1 and R 2 to other percolating systems, it is necessary to consider systems of the same overall shape and boundary condition. Fluctuations in the largest cluster near p c were previously discussed by Coniglio and Stauffer [51][52][53], who showed that s 2 max − s max 2 scales as |p − p c | γ , the same as s max 2 and the susceptibility χ near the critical point, implying that R 2 goes to a finite value. They did not discuss the behavior for p away from p c , nor the shapedependent universality of this quantity.…”

Section: Methodsmentioning

confidence: 61%

Percolation of disordered jammed sphere packings

Ziff

Torquato

2017

J. Phys. A: Math. Theor.

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We determine the site and bond percolation thresholds for a system of disordered jammed sphere packings in the maximally random jammed state, generated by the Torquato-Jiao algorithm. For the site threshold, which gives the fraction of conducting vs. non-conducting spheres necessary for percolation, we find p c = 0.3116(3), consistent with the 1979 value of Powell 0.310(5) and identical within errors to the threshold for the simple-cubic lattice, 0.311608, which shares the same average coordination number of 6. In terms of the volume fraction φ, the threshold corresponds to a critical value φ c = 0.199. For the bond threshold, which apparently was not measured before, we find p c = 0.2424(3). To find these thresholds, we considered two shape-dependent universal ratios involving the size of the largest cluster, fluctuations in that size, and the second moment of the size distribution; we confirmed the ratios' universality by also studying the simple-cubic lattice with a similar cubic boundary. The results are applicable to many problems including conductivity in random mixtures, glass formation, and drug loading in pharmaceutical tablets.

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“…A more rigorous determination of the ratios of critical exponents can be made using finite size scaling relations. As a function of the size N of the system, one expects just on the critical line the behaviors: [13], where ν is the critical exponent associated to the two-point correlation function [7]. These quantities, corresponding to point (b) of the phase diagram, are displayed as a function of N in figure 3.…”

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confidence: 99%