On the study of force-balance percolation

TL;DR

This paper investigates force-balance constrained percolation models, proving a non-trivial percolation threshold, and suggests they share universality with jamming percolation, with implications for understanding phase transitions in correlated systems.

Contribution

It provides rigorous proof of a percolation threshold less than one and links force-balance percolation to jamming percolation through numerical and theoretical analysis.

Findings

Percolation threshold p_c<1 for the models studied.

Transition appears discontinuous with a growing crossover length.

Dynamical exponent similar to sandpile models.

Abstract

We study models of correlated percolation where there are constraints on the occupation of sites that mimic force-balance, i.e. for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We prove rigorously that $p_c<1$ for the two-dimensional models studied. Numerical data indicate that the force-balance percolation transition is discontinuous with a growing crossover length, with perhaps the same form as the jamming percolation models, suggesting the same underlying mechanism driving the transition in both cases. In other words, force-balance percolation and jamming percolation may indeed belong to the same universality class. We find a lower bound for the correlation length in the connected phase and that the correlation function does not appear to be a power law at the transition. Finally, we study the dynamics of the culling procedure invoked to obtain the force-balance configurations and find a dynamical exponent similar to that found in sandpile models.