Connecting perfect one-dimensional leads to sites $i$ and $j$ on the quantum percolation (QP) model, we calculate the transmission coefficient $T_{\mathrm{ij}}\left(E\right)$ at an energy $E$ near the band center and the averages of $\Sigma {\mathrm{ij}}^{}{T}_{\mathrm{ij}}$, $\Sigma {\mathrm{ij}}^{}{r}_{\mathrm{ij}}^2{T}_{\mathrm{ij}}$, and $\Sigma {\mathrm{ij}}^{}{r}_{\mathrm{ij}}^4{T}_{\mathrm{ij}}$ to tenth order in the concentration $p$. In three dimensions, all three series diverge at $p_q{=0.36\mathrm{}}_{-0.02\mathrm{}}^{+0.01\mathrm{}}$, with exponents $\gamma {=0.82\mathrm{}}_{-0.15\mathrm{}}^{+0.10\mathrm{}}$, $\gamma +2\mathrm{}\nu$, and $\gamma +4\mathrm{}\nu$. We find $\nu =0.38\mathrm{}\pm 0.07$, differing from “usual” Anderson localization and violating the bound $\nu \ge 2/d$ of Chayes et al. [Phys. Rev. Lett. 57, 2999 (1986)]. Thus, QP belongs to a new universality class.

• Received 18 July 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.2094