Duality Transformations for Two-Dimensional Directed Percolation and Resistance Problems
- 2 November 1981
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 47 (18) , 1238-1241
- https://doi.org/10.1103/physrevlett.47.1238
Abstract
It is shown that the percolation problem with blocked, one-way, or two-way bonds is self-dual on a square lattice. The usual directed percolation (blocked or one-way bonds) is dual to a simpler process with one- or two-way bonds. The results of a Monte Carlo simulation of the latter are reported and an improved bound on the critical probability is derived. The corresponding resistance problem in which circuit elements have different forward and backward resistances is also shown to be self-dual.Keywords
This publication has 11 references indexed in Scilit:
- Directed Percolation in Two Dimensions: Numerical Analysis and an Exact SolutionPhysical Review Letters, 1981
- Directed percolation: a finite-size renormalisation group approachJournal of Physics A: General Physics, 1981
- Hopping conduction in strong electric fields and directed percolationSolid State Communications, 1981
- Monte Carlo simulation of directed percolation on a square latticeJournal of Physics C: Solid State Physics, 1981
- Directed percolation and Reggeon field theoryJournal of Physics A: General Physics, 1980
- Lower bounds for the critical probability in percolation models with oriented bondsJournal of Applied Probability, 1980
- Percolation theoryReports on Progress in Physics, 1980
- Pair-connectedness for directed bond percolation on some two-dimensional lattices by series methodsJournal of Physics C: Solid State Physics, 1977
- Critical exponents for the conductivity of random resistor latticesPhysical Review B, 1977
- Some Exact Critical Percolation Probabilities for Bond and Site Problems in Two DimensionsPhysical Review Letters, 1963