Ising model with long range correlated disorder on hierarchical lattices

Abstract

A next-neighbor Ising model with disordered but long range correlated coupling constants is investigated. The model is built on a hierarchical lattice and the correlation strength depends on a tuning parameter α. The results are obtained within a transfer-matrix framework, which allows for the evaluation of the properties of individual samples. Collective behavior is computed by averaging over a large number of independent realizations. The dependence of the thermodynamic and magnetic functions with respect to the temperature is investigated for each value of α. Phase diagrams in the (α,T) plane are constructed for two distinct versions of the model, indicating the existence of regions of paramagnetic and ordered phases. Critical values αc, below which the system always assumes the paramagnetic phase, are found for both versions.