Exact solution of a one-dimensional Ising model in a random magnetic field

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. The calculated correlation length agrees with predictions of the Imry-Ma domain argument. © 1983 The American Physical Society.