Topological order in molten antiferromagnets

In this talk, I will discuss the role of antiferromagnetic interactions in two-dimensional crystal melting.  I will show that, for strong enough magnetic interactions, fundamental lattice dislocations become prohibitive due to magnetic frustration.  This gives rise to new types of hexatic and tetratic phases that are topologically ordered, in the sense of containing bound fundamental dislocations and free dislocation pairs.   I will derive these phases through a field-theoretic tretment, and will demonstrate them numerically in an experimentally realizable system of hard spheres confined between parallel plates.  I will discuss the possible survival of antiferromagnetic order in molten crystals.