Phase diagram of a three-dimensional anisotropic long-range Ising model versus temperature and magnetic field

Abstract

The phase diagram of a three-dimensional Ising model in a magnetic field with commensurate and incommensurate phases is studied at low temperature within a mean-field approximation. This analysis was motivated by problems in condensed matter physics concerning, for example, bipolaronic charge-density waves, neutral-to-ionic transitions in organic salts, staging in intercalation compounds, magneto-elastic materials, stacking in discotic liquid crystals, etc. The interactions between the Ising spins are long-range exponentially decaying, and are antiferromagnetic in one direction and ferromagnetic in the perpendicular planes. The ground state of this model is known to be a commensurate or an incommensurate structure with a wavevector that varies as a complete devil's staircase as a function of the magnetic field. Provided some conditions hold on the model parameters, the authors prove rigorously that, for small enough temperature, the mean-field variational form of the model still yields a minimum that is a commensurate or an incommensurate structure, the wavevector of which also varies as a complete devil's staircase as a function of the magnetic field or temperature.