Exact Exponents for the Spin Quantum Hall Transition

We consider the spin quantum Hall transition which may occur in disordered superconductors with unbroken $\mathrm{SU}\left(2\right)$ spin-rotation symmetry but broken time-reversal symmetry. Using supersymmetry, we map a model for this transition onto the two-dimensional percolation problem. The anisotropic limit is an $\mathrm{sl}\left(2\mid 1\right)$ supersymmetric spin chain. The mapping gives exact values for critical exponents associated with disorder averages of several observables in good agreement with recent numerical results.