The random field Ising model on hierarchical lattices

The phase diagram of the random field Ising model defined on the diamond hi erarchical lattices with scaling factor b = 2 and fractal dimension d(f) = 3 is investigated via a combining method encompassing the Migdal-Kadanoff r eal-space renormalization group and an exact recurrence procedure leading t o the local magnetization as a function of the temperature and the local fi elds. Close and above the critical temperature evidences of the formation o f field-induced correlated clusters of reversed spins are found with a size distribution following a power law behavior. The continuous Gaussian and t he discrete delta-bimodal probability distributions for the random fields a re particularly considered but showing no distinct qualitative behavior for low fields. (C) 2001 Elsevier Science B.V. All rights reserved.