Abstract
The Ising chain in a random field is investigated in the region of parameter settings where the measure related to the free-energy distribution is a fractal. The multifractal spectrum is calculated by means of a perturbation expansion in terms of the strength of the random field by exploiting the connection with the problem of a non-natural measure of a one-dimensional map. It is shown that the multifractal spectrum and the distribution of the free-energy fluctuations of finite chains are connected.
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