Elasticity of randomly diluted central force networks under tension

We study the rigidity of two-dimensional site-diluted central force triangular networks under tension. We calculate the shear modulus μ directly and fit it with a power law of the form [Formula presented] where p is the concentration of sites, [Formula presented] its critical value, and f the critical exponent. We find that the critical behavior of μ is quite sensitive to tension. As the tension is increased there is at first a sharp drop in the values of both [Formula presented] and f, followed by a slower decrease towards the values of the diluted Gaussian spring network (or random resistor network). We find that the size of the critical region is also sensitive to tension. The tension-free system has a narrower critical regime with the power law failing for [Formula presented] In contrast, a small tension is sufficient to extend the power law to near [Formula presented] The physical basis for these behaviors is discussed.