1999/05/06 by Marcio Argollo de Menezes, de Menezes, Marcio Argollo, Cristian F. Moukarzel +1
Physics and Astronomy · #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/9905073
RevTeX, 7 pages, uses psfig
arxiv created 1999/05/06 · arxiv updated 2009/11/30
We study directed rigidity percolation (equivalent to directed bootstrap percolation) on three different lattices: square, triangular, and augmented triangular. The first two of these display a first-order transition at p=1, while the augmented triangular lattice shows a continuous transition at a non-trivial pc. On the augmented triangular lattice we find, by extensive numerical simulation, that the directed rigidity percolation transition belongs to the same universality class as directed percolation. The same conclusion is reached by studying its surface critical behavior, i.e. the spreading of rigidity from finite clusters close to a non-rigid wall. Near the discontinuous transition at p=1 on the triangular lattice, we are able to calculate the finite-size behavior of the density of rigid sites analytically. Our results are confirmed by numerical simulation.