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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.
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Grinstein et al. (1983) studied this question.
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