Landau–de Gennes theory

Summary

Landau–de Gennes theory is the Landau theory of nematic liquid crystals. Its order parameter is the Q-tensor, a symmetric traceless $3 \times 3$ matrix that records both the preferred direction of the molecules and the degree of alignment. The free energy is a polynomial in invariants of the Q-tensor plus elastic terms in its gradient. Because a cubic invariant is allowed, the theory predicts a first-order transition between the isotropic and nematic phases. It can also describe defects where the director of the Oseen–Frank theory is undefined.