Relation between the critical exponent of elastic percolation networks and the conductivity and geometrical exponents

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Abstract
The author discusses the relation between the critical behaviour of elastic percolation networks in which the bond-bending forces are present, and that of percolation conductivity. They propose that if the elastic and geometrical thresholds of the network are equal, the critical exponent f of the elastic moduli, is given by, f=t+2 nu , where t is the conductivity exponent and nu the correlation length exponent. This predicts that f(d=2) approximately=3.96, in complete agreement with the most recent and accurate estimate of f. They also discuss the applicability of the present elastic percolation models to real systems such as gels.