PlanarXY-model dynamics in a nematic liquid crystal system

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Abstract
We have constructed a nematic liquid crystal system that exhibits the dynamics of a two-dimensional XY model. The system consists of liquid crystal material placed between two sapphire windows coated with homeotropic alignment material. By holding the windows at two different temperatures, a thermal gradient can be maintained across the liquid crystal material such that the nematic-to-isotropic interface occurs at the center of the cell in a plane parallel to the two window surfaces. The boundary conditions that the interface and one of the windows impose on the nematic phase force the system’s degrees of freedom to be those of the XY model. Comparison between experiment and numerical simulations indicate the system exhibits planar XY-model behavior.