No quasi-long-range order in a two-dimensional liquid crystal

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 cry...

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Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 78; no. 5 Pt 1; p. 051706
Main Authors Paredes V, Ricardo, Fariñas-Sánchez, Ana Isabel, Botet, Robert
Format Journal Article
LanguageEnglish
Published United States 01.11.2008
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Summary: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.
ISSN:1539-3755
DOI:10.1103/PhysRevE.78.051706