Temperature-dependent cubic-quartic Landau free energy ($F=\frac{c}{2}(T^2-T_0^2){\varphi }^2-BT{\varphi }^3+\frac{\lambda }{4}{\varphi }^4$)

For $\varphi \ge 0$ and positive $c,B,\lambda ,T_0$, define $\gamma =2B^2/(\lambda c)$. Completing the square givesFor $0<\gamma <1$, phase coexistence occurs at $T^{\ast }=T_0/\sqrt{1-\gamma }$ with a discontinuous minimum at ${\varphi }^{\ast }=2B{T}^{\ast }/\lambda$. For $\gamma \ge 1$, a nonzero global minimum has lower free energy at every finite temperature. Following the global equilibrium branch then does not force a restoration transition.

When $\gamma \ge 1$ in the stated model, the broken, nonzero minimum remains globally preferred at every finite temperature. A metastable zero state can still exist for $T>T_0$, but its lifetime and a nucleation temperature are kinetic questions. Its disappearance at the spinodal point is not an equilibrium coexistence temperature.

At an equilibrium minimum, $d{F}_{\min }/dT={\partial }_{T}F$ because ${\partial }_{\varphi }F=0$. For $0<\gamma <1$, the entropy decrease at coexistence is $S_0-S_{+}=c(1-\gamma )T^{\ast }({\varphi }^{\ast }{)}^2$. Multiplying by $T^{\ast }$ gives the positive latent heat released on cooling. The units are total heat or heat density according to the normalization of $F$.