  An exact expression for the spin-spin correlation function is derived for the
zero-temperature random-field Ising model defined on a Bethe lattice of
arbitrary coordination number. The correlation length describing dynamic
spin-spin correlations and separated from the intrinsic topological length
scale of the Bethe lattice is shown to diverge as a power law at the critical
point. The critical exponents governing the behaviour of the correlation length
are consistent with the mean-field values found for a hypercubic lattice with
dimension greater than the upper critical dimension.
