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, 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 〈s0sn〉 − 〈s0〉 〈sn〉 in the case that 2J/h is not an integer. The result is a discontinuous function of 2J/h. When p = 2 , we also place a bound on the correlation length of the quenched average of the correlation function 〈s0sn〉. Submitted to: Physical Review B CTP #2202 April 1993 * This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069.