1d random field Ising model and nonlinear dynamics

Abstract

The one-dimensional random field Ising model (1D RFIM) is related to a nonlinear discrete stochastic mapping for an effective local random field which has for nonzero temperature a multifractal measure which may be thin or fat. By means of symbolic dynamics we distinguish parameter regions where the measure at the boundary of the support diverges or goes to zero with infinite to zero slope, respectively. Within the thermodynamic formalism we calculate generalized fractal dimensions as function of physical parameters.

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