Liquid antiferromagnets in two dimensions.

It is shown that, for proper symmetry of the parent lattice, antiferromagnetic order can survive in two-dimensional liquid crystals and even isotropic liquids of pointlike particles, in contradiction to what common sense might suggest. We discuss the requirements for antiferromagnetic order in the absence of translational and/or orientational lattice order. One example is the honeycomb lattice, which upon melting can form a liquid crystal with quasi-long-range orientational and antiferromagnetic order but short-range translational order. The critical properties of such systems are discussed. Finally, we draw conjectures for the three-dimensional case.