Self-organization with equilibration: a model for the intermediate phase in rigidity percolation

TL;DR

This paper introduces a modified self-organization model for rigidity percolation, revealing an intermediate phase with mixed rigidity states, supported by entropy analysis suggesting its potential ubiquity in stress-minimized networks.

Contribution

It presents a new uniform sampling approach for stress-free networks, demonstrating an intermediate phase with both rigid and floppy states in a lattice model.

Findings

Intermediate phase with mixed rigidity states observed

Bond-configurational entropy only slightly lower than random networks

Self-organized phase likely common near rigidity percolation threshold

Abstract

Recent experimental results for covalent glasses suggest the existence of an intermediate phase attributed to the self-organization of the glass network resulting from the tendency to minimize its internal stress. However, the exact nature of this experimentally measured phase remains unclear. We modify a previously proposed model of self-organization by generating a uniform sampling of stress-free networks. In our model, studied on a diluted triangular lattice, an unusual intermediate phase appears, in which both rigid and floppy networks have a chance to occur, a result also observed in a related model on a Bethe lattice by Barre et al. [Phys. Rev. Lett. 94, 208701 (2005)]. Our results for the bond-configurational entropy of self-organized networks, which turns out to be only about 2% lower than that of random networks, suggest that a self-organized intermediate phase could be common in systems near the rigidity percolation threshold.