Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components
Preprint
arXiv:2005.06307
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⁻¹ 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
RP¹ ∼
O(2).
