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

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics

Background:

• Systems with O(2) symmetry exhibit topological transitions in 2D.
• Controversy exists regarding topological transitions in systems with O(3) symmetry.

Purpose of the Study:

• To investigate the presence of a critical point line in the 2D Lebwohl-Lasher model, an example of an O(3) symmetric system.
• To resolve the controversy surrounding topological transitions in O(3) symmetric systems.

Main Methods:

• Analysis of the at-equilibrium order parameter distribution function.
• Application of hyperscaling relations.
• Utilizing first-scaling collapse for probability distribution functions.
• Employing Binder's cumulant.

Main Results:

• Strong evidence indicates the absence of a line of critical points at low temperatures.
• Findings contradict conclusions from several prior numerical studies.
• The Lebwohl-Lasher model in 2D does not exhibit the expected critical behavior for O(3) symmetry.

Conclusions:

• The Lebwohl-Lasher model in 2D lacks a low-temperature critical point line.
• This research provides a definitive resolution to the debate on O(3) symmetric systems and topological transitions.