2019
DOI: 10.1103/physreve.99.012117
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Percolation in a distorted square lattice

Abstract: This paper presents a Monte-Carlo study of percolation in a distorted square lattice, in which, the adjacent sites are not equidistant. Starting with an undistorted lattice, the position of the lattice sites are shifted through a tunable parameter α to create a distorted empty lattice. In this model, two neighboring sites are considered to be connected to each other in order to belong to the same cluster, if both of them are occupied as per the criterion of usual percolation and the distance between them is le… Show more

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Cited by 14 publications
(9 citation statements)
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“…A distorted square lattice was generated by the method of Ref. [23]: each site in the square lattice is shifted by r x and r y in the horizontal and vertical directions, respectively. The two values of r x and r y are chosen from [−α, α] uniformly at random, where the distortion parameter α is not larger than 0.5 when the bond length of the undistorted lattice is 1.…”
Section: Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…A distorted square lattice was generated by the method of Ref. [23]: each site in the square lattice is shifted by r x and r y in the horizontal and vertical directions, respectively. The two values of r x and r y are chosen from [−α, α] uniformly at random, where the distortion parameter α is not larger than 0.5 when the bond length of the undistorted lattice is 1.…”
Section: Methodsmentioning
confidence: 99%
“…A site with a large disc tends to have occupied bonds with its neighbors, and so the occupations of the bonds that are connected to the same site are positively correlated. Mitra et al introduced another percolation with a disorder [23]. In their model, the position of a site on a lattice is randomly shifted on the certain domain that is controlled by an adjustable parameter, and two sites are connected when their Euclidean distance is smaller than a certain distance; thus, the occupations of the bonds that are connected to the same site are negatively correlated.…”
Section: Introductionmentioning
confidence: 99%
“…By examining wrapping probabilities, Wang et al [16,17] simulated the bond and site percolation models on several threedimensional lattices, including simple cubic (SC), the diamond, body-centered cubic (BCC), and face-centered cubic (FCC) lattices. Other recent work on percolation includes [18][19][20][21][22][23][24][25][26][27].…”
mentioning
confidence: 99%
“…where d ij is the distance between pairs of sites (i, j) and n is the number of sites, scales with the number of sites like n ∝ R D where D is the fractal dimension. In two dimensions this has a value at p c of 91/48 = 1.896 independent of the structure of the system [26,[43][44][45][46][47]. Many disordered systems, both discrete [44,45,48] and continuous [43,[49][50][51][52][53] lie in this class, including forest fires, distribution of oil inside porous rock, the diffusion of atoms and conductivity of electrical networks [25,26].…”
Section: Resultsmentioning
confidence: 99%