  We consider the one-dimensional random field Ising model, where the spin-spin
coupling, $J$, is ferromagnetic and the external field is chosen to be $+h$
with probability $p$ and $-h$ with probability $1-p$. At zero temperature, we
calculate an exact expression for the correlation length of the quenched
average of the correlation function $\langle s_0 s_n \rangle - \langle s_0
\rangle \langle s_n \rangle$ in the case that $2J/h$ is not an integer. The
result is a discontinuous function of $2J/h$. When $p = {1 \over 2}$, we also
place a bound on the correlation length of the quenched average of the
correlation function $\langle s_0 s_n \rangle$.
