 Temperature-dependent cubic-quartic Landau free energy

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.