Critical behavior of random resistor networks near the percolation threshold

Abstract

We use low-density series expansions to calculate critical exponents for the behavior of random resistor networks near the percolation threshold as a function of the spatial dimension $d$. By using scaling relations, we obtain values of the conductivity exponent $\mu$. For $d=2\mathrm{}$ we find $\mu =1.43\mathrm{}\pm 0.02$, and for $d=3\mathrm{}$, $\mu =1.95\mathrm{}\pm 0.03$, in excellent agreement with the experimental result of Abeles et al. Our results for high dimensionality agree well with the results of $\epsilon$-expansion calculations.