Order from Disorder: Nonmagnetic Impurities in the Spin-Gap Phase of the Cuprates

We solve the problem of $N$ nonmagnetic impurities in the staggered flux phase of the Heisenberg model which we assume to be a good mean-field approximation for the spin-gap phase of the cuprates. The density of states is evaluated exactly in the unitary scattering limit and is proportional to $1/\omega {ln}^2(|\omega |/D)$, in analogy with the 1D case of doped spin-Peierls and two-leg ladder compounds. We argue that the system exhibits a quasi-long-range order at $T=0\mathrm{}$ with instantaneous spin-spin correlations decreasing as $n_i/{ln}^2\left(n_i{R}_{\mathrm{ij}}\right)$ for large distances $R_{\mathrm{ij}}$ and we predict enhanced low energy fluctuations in neutron scattering.