Superconductivity exponents in two- and three-dimensional percolation

The first transfer-matrix calculation of the superconductivity exponent s of a random mixture of normal and superconducting elements is presented: The exponent s is defined through the divergence of the conductivity as the critical fraction p₂ of superconducting elements is approached: (p-{p₂) }^-s. We obtain very accurate values for the exponents which disagree with the Alexander-Orbach conjecture as well as other conjectures. Our results are s=0. 9770. 010 in two dimensions and s=0. 850. 04 in three dimensions.