Give an outline of the Landau theory of phase transitions for a system with one real order parameter $\phi$. Describe the phase transitions that can be modelled by the Landau potentials (i) $G=\frac{1}{4} \phi^{4}+\frac{1}{2} \varepsilon \phi^{2}$, (ii) $G=\frac{1}{6} \phi^{6}+\frac{1}{4} g \phi^{4}+\frac{1}{2} \varepsilon \phi^{2}$,

where $\varepsilon$ and $g$ are control parameters that depend on the temperature and pressure.

In case (ii), find the curve of first-order phase transitions in the $(g, \varepsilon)$ plane. Find the region where it is possible for superheating to occur. Find also the region where it is possible for supercooling to occur.