1997/05/01 by Cristian F. Moukarzel, Phillip M. Duxbury, P. L. Leath +1 · 5 citations
Materials Science · Physics and Astronomy · #Complex Network Analysis Techniques #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.55.5800
published as Physical Review E 55, 5800 (1997) · RevTeX, 11 pages + 8 .gif figures
openalex publication_date 1997/05/01 · arxiv created 1997/10/13 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Tree models for rigidity percolation, in systems with only central forces, are introduced and solved. A probability vector describes the propagation of rigidity outward from a rigid border. All components of this 'vector order parameter' are singular at the same rigidity threshold pc. The infinite-cluster probability P_\mathrm\ensuremath∞ is usually first order at pc, except in those cases which are equivalent to connectivity percolation. In many cases, P_\mathrm\ensuremath∞\ensuremath∼\ensuremathΔP_\mathrm\ensuremath∞+(p-pc)1/2, indicating critical fluctuations superimposed on the first-order jump (\ensuremathΔP_\mathrm\ensuremath∞). Our tree models for rigidity are in qualitative disagreement with 'constraint-counting' mean-field theories. In an important subclass of tree models 'bootstrap' percolation and rigidity percolation are equivalent.