Absence of universality in percolation models of disordered elastic media with central forces

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Abstract
The authors investigate the universality of scaling laws in elastic percolation networks with central forces. Near the percolation threshold pce the elastic moduli G vanish as G approximately (p-pce)f, and the correlation length xi e diverges as xi e approximately (p-pce)- nu (e), where p is the fraction of active bonds. For bond, correlated bond and site percolation on a triangular network they estimate the ratio f/ nu (e) using Monte Carlo simulations and finite-size scaling analysis, and find f/ nu (e) approximately=1.42, 1.28 and 1.14, respectively. They also find a different value of nu (e) for each of these percolation processes. Therefore, topological and mechanical properties of disordered media with central forces may not have universal properties, and may depend strongly on the microscopic details of the elastic media. These results may also have implications for other vector models of phase transitions.