Construction of nonconvex free energy functions invariant under a symmetry group

In this talk, we will discuss a method to construct nonconvex free energies which are invariant under a (usually discrete) symmetry group and vary with temperature. Applying methods of group and representation theory, this approach yields a formal description of all $C^\infty$ potentials. Using these techniques and geometric arguments, the construction of concrete potentials is comparatively easy. As an example, the cubic-tetragonal phase transition will be discussed; additionally, the problem of growth conditions at infinity will be addressed.