A Dynamical Test of Phase Transition Order: New Things in Old Places.

This is the text of a talk given at various institutions in the past few months. Some form of this talk is to be part of a future book entitled: Nonlinear Aspects of Liquid Crystals: The Open Door. It is written in a tutorial style with students in mind and discusses nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to be fundamentally first order (theory of Halperin, Lubensky and Ma). Our new dynamical tool to test the order of phase transitions that is more than ten times more sensitive than the standard tools of x-ray diffraction and adiabatic calorimetry is described. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of Halperin, Lubensky and Ma.