= Temperature-dependent cubic-quartic Landau free energy
{title2=$F=\frac c2(T^2-T_0^2)\phi^2-BT\phi^3+\frac\lambda4\phi^4$}
For $\phi\geq0$ and positive $c,B,\lambda,T_0$, define $\gamma=2B^2/(\lambda c)$. Completing the square gives
$$
F=\phi^2\left\{\frac\lambda4\left(\phi-\frac{2BT}{\lambda}\right)^2+\frac c2[(1-\gamma)T^2-T_0^2]\right\}.
$$
For $0<\gamma<1$, <phase coexistence> occurs at $T^*=T_0/\sqrt{1-\gamma}$ with a discontinuous minimum at $\phi^*=2BT^*/\lambda$. For $\gamma\geq1$, a nonzero <global minimum> has lower <free energy> at every finite <temperature>. Following the global equilibrium branch then does not force a restoration transition.
Back to article page
