  The following is a thermodynamic analysis of a III order (and some aspects of
a IV order) phase transition. Such a transition can occur in a superconductor
if the normal state is a diamagnet. The equation for a phase boundary in an H-T
(H is the magnetic field, T, the temperature) plane is derived. by considering
two possible forms of the gradient energy, it is possible to construct a field
theory which describes a III or a IV order transition and permits a study of
thermal fluctuations and inhomogeneous order parameters.
