Tricritical Points and Type-Three Phase Transitions

Phase transitions with tricritical points occur in catastrophes generated by sixth-order polynomials. The catastrophe theory of the phase transition is more general than the corresponding Landau theory (at the expense of some of its predictive power) and does not suffer from some of the defects of that theory in its application to systems such as metamagnets, ${\mathrm{He}}^3$-${\mathrm{He}}^4$ solutions, and ferroelectrics. Some consequences of the use of the polynomial—including cubic terms also—are explored.