title: No quasi-long-range order in a two-dimensional liquid crystal.
abstract: Systems with global symmetry group O(2) experience topological transition in the two-dimensional space. But there is controversy about such a transition for systems with global symmetry group O(3). As an example of the latter case, we study the Lebwohl-Lasher model for the two-dimensional liquid crystal, using three different methods independent of the proper values of possible critical exponents. Namely, we analyze the at-equilibrium order parameter distribution function with (1) the hyperscaling relation; (2) the first-scaling collapse for the probability distribution function; and (3) the Binder's cumulant. We give strong evidence for definite lack of a line of critical points at low temperatures in the Lebwohl-Lasher model, contrary to conclusions of a number of previous numerical studies.
authors.affiliation: Centro de Física, Instituto Venezolano de Investigaciones Científicas, Laboratorio de Fisica Estadística Apdo. 20632, Caracas 1020A, Venezuela.
authors.forename: Ricardo
authors.initials: R
authors.lastname: Paredes V
authors.forename: Ana Isabel
authors.initials: AI
authors.lastname: Fariñas-Sánchez
authors.forename: Robert
authors.initials: R
authors.lastname: Botet