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.

• Received 14 January 1983

DOI:https://doi.org/10.1103/PhysRevLett.50.1494