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).
Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components / Delfino, G.; Diouane, Y.; Lamsen, N.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 54:3(2021), pp. 1-10. [10.1088/1751-8121/abd2fc]
Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components
Delfino G.
;Diouane Y.;Lamsen N.
2021-01-01
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).File | Dimensione | Formato | |
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