The Random Field Ising Model on Hierarchical Lattices II: Ground State Critical Properties

The ground state critical properties of the Random Field Ising Model (RFIM) on the diamond hierarchical lattice are investigated via a combining method encompassing real space renormalization group and an exact recurrence procedure. The local magnetization and the nearest neighbors pair correlation function are exactly calculated. The fixed-point joint probability distribution of couplings and local fields are numerically obtained and analyzed, indicating that the critical behavior of the model is governed by the zero temperature disorder fixed point. The critical exponents associated with the order parameter and correlation length are estimated showing an universal behavior regarding the choice of the initial probability distribution for initial local fields being the symmetric continuous Gaussian or discrete delta-bimodal.