= Solution
For $H=0$ and $a<0$, the <free energy> is a symmetric double well. The central stationary point is a maximum; the two stable minima are
$$
\boxed{M_0=\pm\sqrt{-\frac ab},\qquad F_{\min}=-\frac{a^2}{4b}.}
$$
These are the magnetisations of the two symmetry-broken <phases>, selected by an infinitesimal field or a <boundary condition>. An exactly symmetric finite-system ensemble can have $\langle M\rangle=0$ by averaging both wells; that does not make the central maximum a stable homogeneous <phase>.
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