Analytic results for the free energy, magnetic structure factor, and Edwards-Anderson order parameter of a one-dimensional ferromagnetic Ising model in a random magnetic field are obtained. The structure factor consists of both Lorentzian and Lorentzian-squared terms at all temperatures ($T$) greater than zero; the Lorentzian-squared terms vanish at $T=0\mathrm{}$. The calculated correlation length agrees with predictions of the Imry-Ma domain argument.

• Received 27 December 1982

DOI:https://doi.org/10.1103/PhysRevB.27.4503