Coexistence barrier of a cubic-quartic Landau transition ($F_{\mathrm{barrier}}=\lambda v^4/64$)

At coexistence, the landau free energy can factor as $F(\varphi )=\lambda {\varphi }^2(\varphi -v{)}^2/4$. The minima at $0,v$ have equal free energy. Differentiating shows the intermediate maximum at $v/2$, with barrier height $\lambda v^4/64$. The barrier is a local free-energy barrier; predicting spatial nucleation also requires interfacial or gradient information.