Topology invariance in Percolation Thresholds
Serge Galam, Alain Mauger
Abstract
An universal invariant for site and bond percolation thresholds (pcs and pcb respectively) is proposed. The invariant writes pcs1/aspcb-1/ab=δ/d where as, ab and δare positive constants,and d the space dimension. It is independent of the coordination number, thus exhibiting a topology invariance at any d.The formula is checked against a large class of percolation problems, including percolation in non-Bravais lattices and in aperiodic lattices as well as rigid percolation. The invariant is satisfied within a relative error of 5% for all the twenty lattices of our sample at d=2, d=3, plus all hypercubes up to d=6.
Create a lesson
Related papers
Low-temperature magnetism and spin dynamics in the disordered triangular-lattice Yb3+ compound LiCaYb5(BO3)6
Monika Jawale, Saikat Nandi, Prashanta K. Mukharjee et al.
Neural Renormalization Group Flow for Percolation
Anaclara Alvez, Luca Camagna, Sergio Chibbaro et al.
Dynamical phase selection controls compute scaling in looped transformers
Gunn Kim
Semi-localized ground state in a 1D system with long-range hopping
Murod S. Bahovadinov, Faridun N. Jalolov, Vladimir E. Kravtsov et al.
Defect states in three-dimensional diamond photonic band gap crystals
Julia Rocha, Bart A. van Tiggelen, Ad Lagendijk et al.
Disorder-induced conducting edges on Kagomé lattice
A. Chmeruk, D. Jones, L. Chioncel