Probabilistic bond percolation in random arrays

Wintle, H. J.; Puhach, P. A.

doi:10.1007/bf01014479

Cited by 8 publications

(1 citation statement)

References 20 publications

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“…This system has been studied previously, but not with sufficient detail to permit accurate determination of critical exponents (see e.g. Ottavi and Gayda (1974), Pike and Seager (1974), Seager and Pike (1974), Fremlin (1976), Wintle and Puhach (1978)). First, we describe in some detail the system and the simulation method used, and then we present our new results.…”

Section: L292 Letter To the Editormentioning

confidence: 99%

Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs

Gawlinski

Stanley

1981

J. Phys. A: Math. Gen.

261

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Detailed results are reported for the connectivity properties of a system of discs of unit radius free to be situated anywhere within a square of area 2L2. Ordinary lattke percolation would correspond to the discs being situated on the vertices of a J2L x J 2 L lattice. Computer simulations are carried out for a sequence of increasing system sizes ranging from L = 20 to L = 1000; for each value of L a large number of realisations are generated for 25 values of the disc concentration x. We calculate a variety of estimates for the threshold parameter x,, as well as the critical exponents p, y, T and v. Our exponent estimates are in close agreement with accepted values for ordinary lattice percolation; therefore, this continuum system appears to be in the same 'universality class' as lattice percolation.

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Section: L292 Letter To the Editormentioning

confidence: 99%

Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs

Gawlinski

Stanley

1981

J. Phys. A: Math. Gen.

261

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Curie Temperature and Critical Concentration of a Diluted Amorphous Ferromagnet‐ DRPHS Model

Nazarewicz

Zagórski

Ferchmin

et al. 1981

Physica Status Solidi (b)

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and Sektion Physik der Technischen UniversitPt Dresden (c) Curie Temperature and Critical Concentration 1) 2) of a Diluted Amorphous Ferromagnet -DRPHS Model BY W. NAZAREWICZ (a), A. ZAG6RSKI (a), A. R. FEFCHMIN (b), and S. KOBE (c)Ferromagnetism of materials randomly diluted with non-magnetic atoms was subject of many experimental and theoretical studies. Although relevant experiments were performed on crystalline a s well as on amorphous materials, the theory was confined to random dilution of systems with regular lattices, the randomness of interactions being sometimes introduced /l/. However, the related theoretical problems of percolation were recently developed so a s to cover the topologically disordered systems /2 to 7/. The existing experiments / 8 , 9/ were mostly interpreted in t e r m s of actual theories of dilution based originally on the concept of crystallinity of the material, i. e., on the underlying regular lattice. More specifically, for the purpose of calculation the magnetic

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Percolation and cluster distribution. III. Algorithms for the site-bond problem

1979

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Algorithms for estimating the percolation probabilities and cluster size distribution are given in the framework of a Monte Carlo simulation for disordered lattices for the generalized site-bond problem. The site-bond approach is useful when a percolation process cannot be exclusively described in the context of pure site or pure bond percolation. An extended multiple labeling technique (ECMLT) is introduced for the generalized problem. The ECMLT is applied to the site-bond percolation problem for square and triangular lattices. Numerical data are given for lattices containing up to 16 million sites. An application to polymer gelation is suggested.

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Probabilistic bond percolation in random arrays

Cited by 8 publications

References 20 publications

Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs

Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs

Curie Temperature and Critical Concentration of a Diluted Amorphous Ferromagnet‐ DRPHS Model

Percolation and cluster distribution. III. Algorithms for the site-bond problem

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