Anisotropyerature phase diagram for the two-dimensional dipolar Heisenberg model with and without magnetic field

We investigate phase transitions in the two-dimensional dipolar Heisenberg model with uniaxial anisotropy with a specific ratio between the exchange and dipolar constants, δ=1. We obtain the η-T (anisotropy vs temperature) phase diagrams for typical values of magnetic field by a Monte Carlo method with an O(N) algorithm. We find that at lower fields, the η-T phase diagram consists of the planar ferromagnetic (F), perpendicular stripe-ordered (SO), and paramagnetic (P) phases, and is characterized by the triple point. In the SO phase realized at larger η and smaller T, the SO pattern changes depending on the field. On the other hand, we find that at higher fields, the SO phase does not exist, while the planar F phase robustly remains. We study the properties of the phase boundaries in detail. We find that the slope of the spin-reorientation-transition line is positive with and without field, i.e., dηdT>0, which implies that the planar F phase changes to the SO phase with lowering temperature. In the phase diagrams we observe a characteristic shape of the P-planar F phase-transition line, whose maximum point of η is located at an intermediate temperature. This structure leads to the temperature-induced reentrant transition associated with P and planar F phases, which appears in successive phase transitions with lowering temperature: P → planar F → P → SO phase at lower fields and P → planar F → P phases at higher fields.