Phase Transitions as Catastrophes: A Perspective

Abstract

Despite its evident elegance and very beautiful geometrization of a broad spectrum of natural phenomena, catastrophe theory is often charged as being capable of bringing only qualitative insights to various physical processes. Although this charge can no longer be sustained with respect to optics and scattering theory, say, it must be admitted that the application to critical phenomena has been less rewarding. It has been conventional to choose as catastrophe manifold the number-density surface n(P,T), say, with pressure (P) and temperature (T) as control variables. This is a manifestly macroscopic description and, as is well known, leads to the classical mean-field-theory results for critical exponents. Indeed, it now seems that this is all that can ever arise when the problem is formulated in this way, at least without introducing a number of ad hoc extensions.

Richard Merton Visiting Professor of the Deutsche Forchungsgemeinschaft, Universität Tübingen, 1978–79.