Relationship of the Degree of Isotropy of the Thermodynamic Potential Function to the Catastrophe Indices of the Soft Modes whenT→Tc–0

In a previous paper the concept of the catastrophe indices of the soft modes has been introduced for the thermal behavior of the soft modes when the Curie temperature is approached in the ferroic region. In the present paper it is found that if the second to 2 p '-th degree parts of the thermodynamic potential function are isotropic and if one of the soft modes is condensed and the others not, then the catastrophe index of the condensed mode equals 1 and those of the uncondensed modes are ≥ p '. A more detailed theorem is also found.