Quantifying antiferromagnetism in a topologically ordered tetratic

While it is known that the phase transition from solid to liquid phase is a first order phase transition, in two-dimensions there exists a scenario where the melting of a crystal goes through two continuous phase transitions. These transitions follow the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) melting scenario, and are due to the proliferation of topological defects in the crystal.

In a square lattice the intermediate phase that resides between the solid and the liquid phase is called the tetratic phase, at this phase the lattice contains areas with dislocation pairs that are bound together, so that to an observer the lattice looks like a perfect square lattice with areas that contain defects which break the bipartiteness of the lattice. In the special case where the square lattice is strongly antiferromagnetic, the antiferromagnetic nature is “preserved” throughout the melting process. After applying some rules that solve the problem of the broken local bipartiteness in dislocation areas, we have successfully shown the existence of long-range antiferromagnetis order in the tetratic phase.