The Random-Field Ising Model: A Free Energy Study

Abstract

Thermodynamic properties of the random-field Ising model are reviewed and compared with published experimental results on diluted antiferromagnets in a uniform field. The Landau-Ginzburg free energy is calculated in the self-consistent approximation for 3-dimensional systems treating the random field induced fluctuations and the thermodynamic fluctuations of the order parameter separately. At low temperatures and in the presence of random fields two states exist, the stable, long-range ordered state, and the metastable disordered microdomain state. In a heating process, the ordered state changes to the high-temperature phase at the well defined transition temperature. The transition is first order for arbitrarily weak random field. Critical properties are briefly examined and according to the Ginzburg criterion, the classical critical behaviour is predicted for large random fields. For weak fields, nonclassical critical behaviour is expected.