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 $\alpha$ 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 less than or equal to a certain value, called connection threshold $d$. While spanning becomes difficult in distorted lattices as is manifested by the increment of the percolation threshold $p_c$ with $\alpha$, an increased connection threshold $d$ makes it easier for the system to percolate. The scaling behavior of the order parameter through relevant critical exponents and the fractal dimension $d_f$ of the percolating cluster at $p_c$ indicate that this new type of percolation may belong to the same universality class as ordinary percolation. This model can be very useful in various realistic applications since it is almost impossible to find a natural system that is perfectly ordered.

6 pages, 5 figures

References in corpus (17)

• Network robustness and fragility: Percolation on random graphs
• Clique percolation in random networks
• Recent advances in percolation theory and its applications
• Exact exponents for the spin quantum Hall transition
• Percolation Transitions in Scale-Free Networks under Achlioptas Process
• Bond and Site Percolation in Three Dimensions
• Recent advances and open challenges in percolation
• Local cluster aggregation models of explosive percolation
• Self-stabilised fractality of sea-coasts through damped erosion
• Width of percolation transition in complex networks
• Casimir-like forces at the percolation transition
• Percolation description of the global topography of Earth and Moon
• Critical and Topological Properties of Cluster Boundaries in the $3d$ Ising Model
• Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations
• New universality class in percolation on multifractal scale-free planar stochastic lattice
• Geometrical Phase Transition on WO${}_3$ Surface
• Percolation model with an additional source of disorder

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• Universality of random-site percolation thresholds for two-dimensional complex non-compact neighborhoods
• Percolation of systems having hyperuniformity or giant number-fluctuations
• Bond percolation in distorted square and triangular lattices
• Bond percolation in distorted simple cubic and body-centered cubic lattices
• Site and bond percolation in linearly distorted triangular and square lattices