Antiferromagnetism and superconductivity in UPt₃

The short-ranged antiferromagnetism recently seen in UPt₃ is proved incompatible with two-dimensional (2D) order parameter models that take the antiferromagnetism as a symmetry-breaking field. To adjust to the local moment direction, the order parameter twists over very long length scales as per the Imry-Ma argument. A variational solution to the Ginzburg-Landau equations is used to study the nature of the short-range superconducting order. Although there are still two transitions, the lower one is of first order - in contradiction to experiments. It is shown that the latent heat predicted by the 2D models at the lower transition is too large no to have been seen. A simple periodic model is numerically studied to show that the second transition cannot be a crossover either.