Catastrophe Theory and Phase Transitions : Topological Aspects of Phase Transtions and Critical Phenomena

Catastrophe theory, which treats the singularities of smooth real-valued functions, refers to the unexpectedness of discontinous effects produced by continuos causes. Examples of this behaviour can be found throughout contemporary science. This theory can unify concepts and nomenclatures which have been in disarray for a long time because of their independent development in different scientific fields. Also, Catastrophe Theory emphazises metastable states, whereas rigorous statistical mechanics does not, and even denies their existence.