Singularities near critical and tricritical end points: thermodynamics and applications

Systems where a phase transition is induced by biquadratic coupling of two different modes, like some types of ferroelectric materials, are analyzed utilizing a Landau-type free energy. The phase diagram associated with this free energy has a critical line that meets a first-order phase boundary surface at a point that can be either a critical end point or a tricritical end point. Scaling arguments indicate that, close to a critical or to a tricical end ppoint, the first-order phase boundaries exhibit nonanalyticities associated with the singularities of that critical line or of that tricritical point. Explicit expressions for the phase boundaries in the model for ferroelectric materials are computed and checked for singularities. The association with the nonanalyticities of the critical line and of the tricritical point is also verified, confirming our phenomenological predictions.