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The one-dimensional Ising model in a random field is studied with use of a functional recursion relation. For temperatures exceeding a given value, the fixed function of the relation is found and shown to be a devil's staircase. From this result it is possible to evaluate the free energy to arbitrary precision. In the field-strength-temperature plane, a crossover line corresponding to the onset of frustration is found.
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Bruinsma et al. (1983) studied this question.
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