= Solution
In the <Landau theory> approximation, choose the <global minimum> of the <Landau free energy> as a function of the <magnetization>. Since $\mathcal A_6>0$, the <polynomial> is a <coercive function> and a <global minimum> exists. The candidates are <stationary points> satisfying
$$
\boxed{\mathcal A_2m+\mathcal A_4m^3+\mathcal A_6m^5=h.}
$$
Check their values of the <free-energy density>; a <stationary point> or a <metastable> <local minimum> alone need not be the equilibrium state. Positive curvature $\mathcal A_2+3\mathcal A_4m^2+5\mathcal A_6m^4$ ensures local stability; when it vanishes, higher terms must be checked. The selected <global minimum> is the <equilibrium magnetization> within this approximation.
At zero <magnetic field>, equal opposite minima describe distinct phases exhibiting <spontaneous symmetry breaking>. A <spontaneous magnetization> is obtained by taking the <thermodynamic limit> before $h\to0^+$ or $h\to0^-$. A symmetric finite-volume average can instead have zero <expectation> even when the minima are nonzero. Thus one must specify the phase when interpreting the minimizer as the equilibrium <expectation>.
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