  We present results of numerical studies of spin quantum Hall transitions in
disordered superconductors, in which the pairing order parameter breaks
time-reversal symmetry. We focus mainly on p-wave superconductors in which one
of the spin components is conserved. The transport properties of the system are
studied by numerically diagonalizing pairing Hamiltonians on a lattice, and by
calculating the Chern and Thouless numbers of the quasiparticle states. We find
that in the presence of disorder, (spin-)current carrying states exist only at
discrete critical energies in the thermodynamic limit, and the spin-quantum
Hall transition driven by an external Zeeman field has the same critical
behavior as the usual integer quantum Hall transition of non-interacting
electrons. These critical energies merge and disappear as disorder strength
increases, in a manner similar to those in lattice models for integer quantum
Hall transition.
