@article{bibcite_648,
  author = {Gesualdo Delfino and Youness Diouane and Noel M. Lamsen},
  title = {Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components},
  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 <em>N</em> director components (<em>RP</em>ᴺ$^{-}${\textonesuperior} model), which yields the Lebwohl-Lasher model for <em>N</em> = 3. For <em>N</em> > 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 <em>O</em>(<em>N</em>(<em>N</em> + 1)/2 - 1) model. For <em>N</em> = 2 the fixed point equations yield the Berezinskii-Kosterlitz-Thouless transition required by the correspondence <em>RP</em>{\textonesuperior} \~ <em>O</em>(2).},
  year = {2020},
  journal = {J. Phys. A Math. Theor.},
  volume = {54},
  pages = {03LT01},
  url = {https://iopscience.iop.org/article/10.1088/1751-8121/abd2fc},
  doi = {10.1088/1751-8121/abd2fc},
}