XY model defects in a 2D nematic field. Topological defects with winding numbers +1/2 and −1/2 form, annihilate, and self-organize via the Kibble-Zurek mechanism.
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Defects: —
Free energy: —
Nematic liquid crystal: director field n(x) with n ≡ −n (headless). Defects have half-integer winding: s = ±1/2.
Kibble-Zurek (1976/1985): rapid quench through transition → topological defects freeze in. Density ~ quench rate.