Analytical approximation of the site percolation thresholds for monomers and dimers on two-dimensional lattices
Sign Up to like & getrecommendations! Published in 2019 at "Physica A: Statistical Mechanics and its Applications"
DOI: 10.1016/j.physa.2018.10.023
Abstract: Abstract In this paper, a theoretical approach to calculate site percolation thresholds on two-dimensional lattices is proposed. The method, based on exact counting of configurations on finite cells, arises as a generalization of the analytical… read more here.
Keywords: dimensional lattices; analytical approximation; site percolation; percolation thresholds ... See more keywords
Random site percolation on honeycomb lattices with complex neighborhoods.
Sign Up to like & getrecommendations! Published in 2022 at "Chaos"
DOI: 10.1063/5.0099066
Abstract: We present a rough estimation-up to four significant digits, based on the scaling hypothesis and the probability of belonging to the largest cluster vs the occupation probability-of the critical occupation probabilities for the random site… read more here.
Keywords: complex neighborhoods; random site; site percolation; honeycomb ... See more keywords
Exact percolation probabilities for a square lattice: site percolation on a plane, cylinder, and torus
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ac61b8
Abstract: We have found analytical expressions (polynomials) of the percolation probability for site percolation on a square lattice of size L × L sites when considering a plane (the crossing probability in a given direction), a… read more here.
Keywords: plane; cylinder; probability; torus ... See more keywords
Redefinition of site percolation in light of entropy and the second law of thermodynamics.
Sign Up to like & getrecommendations! Published in 2019 at "Physical review. E"
DOI: 10.1103/physreve.100.062109
Abstract: In this article, we revisit random site and bond percolation in a square lattice, focusing primarily on the behavior of entropy and the order parameter. In the case of traditional site percolation, we find that… read more here.
Keywords: percolation light; redefinition site; site; thermodynamics ... See more keywords
Dynamics around the site percolation threshold on high-dimensional hypercubic lattices.
Sign Up to like & getrecommendations! Published in 2019 at "Physical review. E"
DOI: 10.1103/physreve.99.022118
Abstract: Recent advances on the glass problem motivate reexamining classical models of percolation. Here we consider the displacement of an ant in a labyrinth near the percolation threshold on cubic lattices both below and above the… read more here.
Keywords: dynamics around; percolation threshold; around site; percolation ... See more keywords
Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense
Sign Up to like & getrecommendations! Published in 2021 at "Electronic Journal of Probability"
DOI: 10.1214/21-ejp659
Abstract: Recent works have shown that random triangulations decorated by critical ($p=1/2$) Bernoulli site percolation converge in the scaling limit to a $\sqrt{8/3}$-Liouville quantum gravity (LQG) surface (equivalently, a Brownian surface) decorated by SLE$_6$ in two… read more here.
Keywords: random triangulations; metric peanosphere; site percolation; percolation ... See more keywords
A Boltzmann Approach to Percolation on Random Triangulations
Sign Up to like & getrecommendations! Published in 2019 at "Canadian Journal of Mathematics"
DOI: 10.4153/cjm-2018-009-x
Abstract: Abstract We study the percolation model on Boltzmann triangulations using a generating function approach. More precisely, we consider a Boltzmann model on the set of finite planar triangulations, together with a percolation configuration (either site-percolation… read more here.
Keywords: site percolation; bond percolation; approach; approach percolation ... See more keywords