More Complicated Systems

Abstract

Although the description presented in Chaps. 2–7 lays out a rich picture of a phase transformation, it is not rich enough to describe most of the transformations that we find around us. The problem is that so far we have been looking at the systems that can be described by a scalar, one-component order parameter while order parameters of real transformations may have many components or essential internal symmetry, not captured by a simple scalar. A few examples of more complicated systems are considered in this chapter. Specifically, we are looking at the systems where the order parameter is subject to a conservation law and go over all major steps of the method deriving the equilibrium equations in homogeneous and heterogeneous systems, dynamic equation, and analyzing the role of fluctuations. We lay out the phenomenological theory of superconductivity where the OP is a complex number and demonstrate how the method can help in calculating different properties of a superconductor. A section is devoted to a system that undergoes crystallographic transformation described by the OP that has more than one component, which interact with each other. We also look at the systems which have long time-correlation property—memory or are described by two fields of completely different symmetries.