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 〈${\mathit{s}}_0$${\mathit{s}}_{\mathit{n}}$〉-〈${\mathit{s}}_0$〉〈${\mathit{s}}_{\mathit{n}}$〉 in the case that 2J/h is not an integer. The result is a discontinuous function of 2J/h. When p=1/2, we also place a bound on the correlation length of the quenched average of the correlation function 〈${\mathit{s}}_0$${\mathit{s}}_{\mathit{n}}$〉.

• Received 30 April 1993

DOI:https://doi.org/10.1103/PhysRevB.48.9508