Analytical explanation of a phase transition in the multifractal measure connected with a one-dimensional random field Ising model

Abstract

In certain one-dimensional stochastic mappings a sharp drop of the D_q-spectrum of fractal dimensions for negative values of q is observed at a spacial value of the noise strength. This transition is connected to the vanishing of deep valleys in the measure and can be understood by analyzing the contribution of periodic orbits. A special example is given by the one-dimensional Ising model in a bimodal random field.

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