"Weak Lifshitz condition" and the allowed types of ordering in second-order phase transitions

Abstract

It is known that the Lifshitz condition is not a necessary condition for second-order phase transitions in crystals. We show, however, that a certain necessary condition (which we have termed "the weak Lifshitz condition") does exist, though much weaker than the original Lifshitz condition. This necessary condition imposes certain restrictions on the allowed irreducible, or physically irreducible, representations associated with the transition, and accordingly, on the allowed types of ordering below the transition.