Nematic order, topological defects, and Frank elastic energy
Temperature0.15
Elastic Constant1.0
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Liquid crystals are partially ordered phases — molecules have orientational order but not positional order. The nematic director n̂(r) is a unit vector field describing local average alignment (n̂ ≡ −n̂, so the order parameter is a tensor Q = ½(3n̂n̂ − I)). The Frank elastic energy penalizes splay, twist, and bend distortions: F = ½K[(∇·n̂)² + (n̂×∇×n̂)²]. The simulation uses a XY-like model with headless spins. Topological defects (±½ disclinations) are topologically protected — they cannot be smoothly removed.