Correlation functions of the one-dimensional random-field Ising model at zero temperature.

We consider the one-dimensional random-field Ising model, where the spin-spin coupling [ital J] is ferromagnetic and the external field is chosen to be +[ital h] with probability [ital p] and [minus][ital h] with probability 1[minus][ital p]. At zero temperature, we calculate an exact expression for the correlation length of the quenched average of the correlation function [l angle][ital s][sub 0][ital s[ital n]][r angle][minus][l angle][ital s][sub 0][r angle][l angle][ital s][sub [ital n]][r angle] in the case that 2[ital J]/[ital h] is not an integer. The result is a discontinuous function of 2[ital J]/[ital h]. When [ital p]=1/2, we also place a bound on the correlation length of the quenched average of the correlation function [l angle][ital s][sub 0][ital s[ital n]][r angle].