Coexistence barrier of a cubic-quartic Landau transition
= Coexistence barrier of a cubic-quartic Landau transition
{title2=$F_{\rm barrier}=\lambda v^4/64$}
At coexistence, the <landau free energy> can factor as $F(\phi)=\lambda\phi^2(\phi-v)^2/4$. 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.