Anisotropic long-range Ising model in a magnetic field

Abstract

Motivated by different physical contexts (bipolaronic theory of charge density waves, neutral-ionic transition in organic salts, staging in intercalation compounds) we have studied a 3d Ising model in a field, where the interaction is long-range AFM in the x-direction and FM inside the perpendicular planes. Below the 2d Ising transition temperature, the FM interaction can be safely handled within the mean field approximation, but frustration between long-range AFM interactions leads to modulated phases. We have rigorously proved that at low temperatures and rapidly enough decaying interactions the modulation wavevector versus field is a Devil's Staircase. Outside that region the complete phase diagram has been computed with two different methods: (1) high-precision numerical algorithm based on the method of effective potentials; (2) parabolic approximation leading to an exactly solvable model.