Evidence for a topological transition in nematic-to-isotropic phase transition in two dimensions

The nematic-to-isotropic orientational phase transition, or equivalently the $RP^2$ model, is considered in two dimensions and the question of the nature of the phase transition is addressed. Using powerful conformal techniques adapted to the investigation of critical properties of two-dimensional scale-invariant systems, we report strong evidences for a transition governed by topological defects analogous to the Berezinskii-Kosterlitz-Thouless transition in two-dimensional XY model.