= Landau-de Gennes free energy
{c}
{title2=$f(Q)$}
The Landau-de Gennes free energy is a <rotational symmetry> preserving <Landau free energy> of the <nematic order parameter>. One three-dimensional normalization through fourth order is
$$
f(Q)=\frac a2\operatorname{Tr}Q^2+\frac c3\operatorname{Tr}Q^3+\frac b4(\operatorname{Tr}Q^2)^2,
\qquad b>0.
$$
The cubic invariant generically produces a <first-order phase transition>. Its absence in two dimensions is an algebraic identity, not a guarantee that a <mean-field approximation> captures all fluctuations.
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