Correlated two-component percolation

Petrov, I. V.; Stoynev, I.I.; Babalievskii, F V

doi:10.1088/0305-4470/24/18/026

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…Similar checks for bi-colored lattices with N 2 and N 3 neighborhoods were performed in Ref. 24. For sites reconstruction process, when x = 0 or x = p c (N 2 ), the difference between originally used N 2 sites and their N 3 and/or N 4 substitutes vanishes:…”

Section: Table Imentioning

confidence: 83%

Restoring site percolation on damaged square lattices

Malarz

2005

Phys. Rev. E

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Restoring site percolation on a damaged square lattice with the nearest neighbor (N2) is investigated using two different strategies. In the first one, a density y of new sites are created on the empty sites with longer range links, either next-nearest neighbor (N3) or next-next-nearest neighbor (N4), but without N2. In the second one, new longer range links N3 or N4 are added to N2 but only for a fraction v of the remaining non-destroyed sites. Starting at p(c)(N2), with a density x of randomly destroyed sites, the values of y(c) and v(c), which restore site percolation, are calculated for both strategies with, respectively, N3 and N4 using Monte Carlo simulations. Results are obtained for the whole range 0 < or = x < or = p(c)(N2).

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Section: Table Imentioning

confidence: 83%

Restoring site percolation on damaged square lattices

Malarz

2005

Phys. Rev. E

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“…In parallel, not much work has been devoted to regular lattices with neighbor interactions which are not nearest neighbors (N 2 , von Neumann's neighborhood). Some scarce results are available for simultaneous nearest and next nearest neighbors (N 2 +N 3 , Moore's neighborhood) [4,11].…”

Section: Introductionmentioning

confidence: 99%

Square-lattice site percolation at increasing ranges of neighbor bonds

Malarz

Galam

2005

Phys. Rev. E

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We report site percolation thresholds for square lattice with neighbor bonds at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (NN), next-nearest neighbors (NNN), next-next-nearest neighbors (4N), and fifth-nearest neighbors (6N) yield the same pc = 0.592... . The fourth-nearest neighbors (5N) give pc = 0.298... . This equality is proved to be mathematically exact using symmetry argument. We then consider combinations of various kinds of neighborhoods with (NN+NNN), (NN+4N), (NN+NNN+4N), and (NN+5N). The calculated associated thresholds are respectively pc = 0.407..., 0.337..., 0.288..., and 0.234... . The existing Galam-Mauger universal formula for percolation thresholds does not reproduce the data showing dimension and coordination number are not sufficient to build a universal law which extends to complex lattices.

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“…In the percolation theory [13,14], the fundamental factors that determines the percolation threshold p c is lattice connectivity and whether the process is site process or bond process. In the present case (square lattice with diagonal connectivity and site process), it is known that the percolation threshold is p c = 0.407 • • • [13,15].…”

Section: Brief Summary For Repulsive Impurity Potentialmentioning

confidence: 74%

Metallization of Mott Insulators through Percolation in Partially Filled Impurity Hubbard Model

Yokoyama

Sato

Kono

et al. 2020

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019)

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An impurity Hubbard model with strong correlation on a square lattice with diagonal hopping is studied for an antiferromagnetic state, using a variational Monte Carlo method. If the impurity potential is repulsive with moderate strength and the density of impurity sites is equal to or larger than the doping rate in a partially filled band, the state becomes insulating. When the impurity density is increased, an insulator-to-metal transition takes place through a mechanism of percolation.

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Correlated two-component percolation

Cited by 8 publications

References 11 publications

Restoring site percolation on damaged square lattices

Restoring site percolation on damaged square lattices

Square-lattice site percolation at increasing ranges of neighbor bonds

Metallization of Mott Insulators through Percolation in Partially Filled Impurity Hubbard Model

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