The random field Ising model on hierarchical lattices

Abstract

The phase diagram of the random field Ising model defined on the diamond hierarchical lattices with scaling factor b=2 and fractal dimension d f=3 is investigated via a combining method encompassing the Migdal–Kadanoff real-space renormalization group and an exact recurrence procedure leading to the local magnetization as a function of the temperature and the local fields. Close and above the critical temperature evidences of the formation of field-induced correlated clusters of reversed spins are found with a size distribution following a power law behavior. The continuous Gaussian and the discrete delta-bimodal probability distributions for the random fields are particularly considered but showing no distinct qualitative behavior for low fields.