We know first order phase transitions, like second order transitions, also have order parameters. They too can be dealt with Landau theory.
What kind of temperature dependence of the order parameter (a discontinuous step function?) is needed to explain a discontinuous phase transition?
How is that functional dependence achieved through Landau's approach to phase transition?
What is the physical way of understanding such discontinuous change within the arena of Landau theory? Is it some kind of tunnelling that happens between the minima of free energy?