Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2008-06-10
Physics
Condensed Matter
Disordered Systems and Neural Networks
15 pages, 32 figures
Scientific paper
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.
Jeng Monwhea
Schwarz J.-M.
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