= Solution
<Landau-Ginzburg theory> assumes a local <gradient expansion> for a slowly varying <order parameter>. At zero field the microscopic spin-flip symmetry sends $m\mapsto-m$, so only even powers occur. <Rotational symmetry> makes the leading derivative term $(\nabla m)^2$, while locality and analyticity near the transition organize higher powers and derivatives. Stability requires a positive gradient coefficient and, at an ordinary continuous transition, $\alpha_4(T_c)>0$; the coefficient $\alpha_2(T)$ changes sign at $T_c$.
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