Fractal measures in the random-field Ising model

Abstract

The measure of the local field probability density in the discrete (+or-h) short-ranged coupled random-field Ising chain is studied with the use of a specific discrete one-dimensional map. The strange set corresponding to this measure resembles Cantor sets and its full scaling properties are computed by evaluating the generalised fractal dimensions Dq and the spectrum of singularities f( alpha ). The main results are also derived by perturbation theory valid for weak fields h.