@article {657, title = {Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components}, journal = {J. Phys. A Math. Theor.}, volume = {54}, year = {2020}, pages = {03LT01}, abstract = {The Lebwohl-Lasher model describes the isotropic-nematic transition in liquid crystals. In two dimensions, where its continuous symmetry cannot break spontaneously, it is investigated numerically since decades to verify, in particular, the conjecture of a topological transition leading to a nematic phase with quasi-long-range order. We use scale invariant scattering theory to exactly determine the renormalization group fixed points in the general case of N director components (RPᴺ$^{-}${\textonesuperior} model), which yields the Lebwohl-Lasher model for N = 3. For N > 2 we show the absence of quasi-long-range order and the presence of a zero temperature critical point in the universality class of the O(N(N + 1)/2 - 1) model. For N = 2 the fixed point equations yield the Berezinskii-Kosterlitz-Thouless transition required by the correspondence RP{\textonesuperior} \~{} O(2).}, doi = {10.1088/1751-8121/abd2fc}, url = {https://iopscience.iop.org/article/10.1088/1751-8121/abd2fc}, author = {Gesualdo Delfino and Youness Diouane and Noel Lamsen} }