Theorems Relating to Catastrophe Indices and to the “Fourth” Checkpoint for Second-Order Transitions

Abstract

Firstly the meaning of catastrophe indices and of the “fourth” checkpoint for second-order transitions are explained over again. And then three new theorems are presented. The first of them is most fundamental from which the two others follow. The second theorem is: The catastrophe indices of a transition parameter system always include a unity. The third theorem is: If the dimensionality of the irreducible representation for the transition parameters is lower than 3, the transition from the prototypic to a ferroic phase always passes the “fourth” checkpoint.