= Solution
An <order parameter> distinguishes phases through a macroscopic observable, such as the mean spin $m$ of a ferromagnet. Its vanishing can reflect an unbroken symmetry, while choosing one of several nonzero equilibrium values gives <spontaneous symmetry breaking>. <Landau-Ginzburg theory> treats it as a slowly varying field and expands the <free energy> in terms allowed by symmetry:
$$
\mathcal A[m]=\int d^Dx\left[\frac K2|\nabla m|^2+\frac r2m^2+\frac u4m^4+\frac v6m^6-hm\right].
$$
Here $K>0$ penalizes spatial variation, $h$ is the conjugate field, and the highest retained even coefficient must stabilize large $|m|$. For a spin-flip-symmetric system, odd powers are forbidden at $h=0$. Equilibrium in the <Landau approximation> minimizes this functional; near an ordinary continuous transition $r=r_t t$ with $t=(T-T_c)/T_c$ and $r_t>0$.
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