Lack of reentrance in randomly frustrated three-dimensional XY ferromagnets

A Migdal-Kadanoff real-space renormalization-group method is used to study two nearest-neighbor randomly frustrated XY ferromagnets in three dimensions. The models are an XY ferromagnet with a dilute concentration of antiferromagnetic exchange couplings and an XY ferromagnet with random Dzyaloshinskii-Moriya spin-orbit interactions. The purpose of the investigation is to examine whether these two systems exhibit reentrance, characterized by the loss of long-range ferromagnetic order upon cooling and subsequent appearance of either a paramagnetic or a spin-glass phase. Unlike claims in the literature concerning reentrant behavior for two-dimensional versions of the systems considered here, we do not find any evidence for reentrance for these models in three dimensions. We propose two possible mechanisms for reentrance in three-dimensional dilute magnetic vector-spin systems.