Elasticity of highly cross-linked random networks

Starting from a microscopic model of randomly cross-linked particles with quenched disorder, we calculate the Landau-Wilson free energy for arbitrary cross-link densities. Considering pure shear deformations, takes the form of the elastic energy of an isotropic amorphous solid state, from which the shear modulus can be identified. It is found to be a universal quantity, not depending on any microscopic length-scales of the model.