Dynamic Monte Carlo study of rigidity percolation using an event-based ensemble approach

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Materials Science

Background:

• Rigidity percolation is key to understanding mechanical stability in disordered materials.
• Previous studies primarily focused on static properties, neglecting the dynamics of rigidity transitions.
• The dynamics of rigidity transitions on lattices, particularly the triangular lattice, are less explored.

Purpose of the Study:

• To investigate the dynamics of rigidity transitions on a triangular lattice.
• To develop an efficient dynamic algorithm for monitoring rigid cluster evolution.
• To uncover novel dynamic properties and improve critical parameter estimations.

Main Methods:

• Formulation of a dynamic pebble game algorithm for sequential bond addition.
• Monitoring cluster emergence, evolution, and merger events.
• Utilizing an event-based ensemble approach for high-precision measurements.

Main Results:

• Discovery of overlooked temporal self-similarity in cluster dynamics.
• Identification of large-scale cascade events triggered by single bond additions.
• High-precision estimates for critical point (p_c=0.6602778(10)), inverse correlation-length exponent (1/ν=0.850(3)), and fractal dimension (d_f=1.850(2)).

Conclusions:

• The dynamic pebble game offers computational efficiency comparable to static methods.
• Temporal self-similarity and cascade events are crucial features of rigidity transitions.
• The obtained critical parameters significantly refine existing values, advancing the understanding of disordered materials.