Percolation on two- and three-dimensional lattices

Abstract

In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolation are studied on a number of lattices in two and three dimensions. Quite good results for the wrapping probabilities, correlation length critical exponent and critical concentration are obtained for the square, simple cubic, HCP and hexagonal lattices by using relatively small systems. We also confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.

15 pages, 6 figures, 3 tables

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• Worm-algorithm-type Simulation of Quantum Transverse-Field Ising Model
• Geometric properties of the Fortuin-Kasteleyn representation of the Ising model
• Percolation thresholds on 3-dimensional lattices with 3 nearest neighbors
• Stacked triangular lattice: Percolation properties
• Percolation transition of hydration water at hydrophilic surfaces
• Newman-Ziff algorithm for the bootstrap percolation: application to the Archimedean lattices
• Site percolation on lattices with low average coordination numbers
• Percolation of the two-dimensional XY model in the flow representation
• Universality class of the percolation in two-dimensional lattices with distortion
• Bootstrap and diffusion percolation transitions in three-dimensional lattices
• Geometric clusters in the overlap of the Ising model
• Obtaining Stiffness Exponents from Bond-diluted Lattice Spin Glasses
• Crossover from string to cluster dynamics following a field quench in spin ice
• Transfer-matrix approach to the three-dimensional bond percolation: An application of Novotny's formalism
• Bond percolation in distorted simple cubic and body-centered cubic lattices
• Low-Temperature Phase Boundary of dilute Lattice Spin Glasses
• Percolation model for structural phase transitions in Li${}_{1-x}$H${}_x$IO${}_3$ mixed crystals