Past exam of the thermal and statistical physics course of the University of Cambridge / 2013 / Paper 1 / 4 / ii

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 areThese 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 $⟨M⟩=0$ by averaging both wells; that does not make the central maximum a stable homogeneous phase.