  The non-equilibrium dynamics of the strongly diluted random-bond Ising model
in two-dimensions (2d) is investigated numerically.
  The persistence probability, P(t), of spins which do not flip by time t is
found to decay to a non-zero, dilution-dependent, value $P(\infty)$. We find
that $p(t)=P(t)-P(\infty)$ decays exponentially to zero at large times.
Furthermore, the fraction of spins which never flip is a monotonically
increasing function over the range of bond-dilution considered. Our findings,
which are consistent with a recent result of Newman and Stein, suggest that
persistence in disordered and pure systems falls into different classes.
Furthermore, its behaviour would also appear to depend crucially on the
strength of the dilution present.
