Year: 1997
Type: article
Abstract: 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 ${\mathrm{p}}_{\mathrm{c}}$. The infinite-cluster probability ${\mathrm{P}}_{\mathrm{\ensuremath{\infty}}}$ is usually first order at ${\mathrm{p}}_{\mathrm{c}}$, except in those cases which are equivalent to connectivity percolation. In many cases, ${\mathrm{P}}_{\mathrm{\ensuremath{\infty}}}$\ensuremath{\sim}\ensuremath{\Delta}${\mathrm{P}}_{\mathrm{\ensuremath{\infty}}}$+(p-${\mathrm{p}}_{\mathrm{c}}$${)}^{1\mathrm{/}2}$, indicating critical fluctuations superimposed on the first-order jump (\ensuremath{\Delta}${\mathrm{P}}_{\mathrm{\ensuremath{\infty}}}$). 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.
Authors: C. Moukarzel, P. M. Duxbury, P. L. Leath
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1990837659