Two-dimensionalXYmagnets with random Dzyaloshinskii-Moriya interactions

Two-dimensional $\mathrm{XY}$ ferromagnets with random Dzyaloshinskii-Moriya interactions are studied. Such systems can be mapped onto a Coulomb gas with a quenched random array of dipoles. For large amounts of randomness, the low-temperature phase of the $\mathrm{XY}$ model is destroyed entirely. For small amounts of randomness, the behavior with decreasing temperatures is first paramagnetic, then ferromagnetic, and finally becomes paramagnetic again via a second, reentrant phase transition. These phase transitions are driven by an unbinding of vortices, just as in pure $\mathrm{XY}$ models. In contrast to pure $\mathrm{XY}$ models, the exponent $\eta$ and the spin-wave stiffness are nonuniversal at $T_c$. The reentrant phase transitions appear to persist when the model is continued to $2+\epsilon$ dimensions. Similar results should apply to spin-glass models with a small concentration of bonds with the wrong sign.