Random-field Ising model on hierarchical lattices: thermodynamics and ground-state critical properties

The phase diagram, the thermodynamic and ground-state critical properties of the random-field Ising model defined on the diamond family of hierarchical lattices with arbitrary dimension and scaling factor b=2 is investigated. The continuous Gaussian and the discrete delta-bimodal initial symmetric probability distributions for the random fields are particularly considered. The thermodynamics potentials (internal energy, specific heat and magnetization) are calculated by an exact recurrence procedure and analyzed as a function of the temperature and the random field strength. The phase diagram is drawn and explored close to the ferromagnetic–paramagnetic transition where evidences of the formation of stable field-induced correlated clusters of reversed spins are observed. The ground-state properties (critical fields, fixed-point probability distribution, magnetization and critical exponents) are also investigated and fully analyzed. None of the thermodynamics potentials studied present strong qualitative distinct features and a universal critical behavior is achieved whenever the continuous or the discrete random-field probability distribution is considered.