Landau, Lifshitz, and weak Lifshitz conditions in the Landau theory of phase transitions in solids

Abstract

Landau theory provides a group-theoretical method for determining which symmetry changes can occur in second-order phase transitions in solids. The irreducible representations of the space group of the higher-symmetry phase must satisfy certain conditions. For transitions to commensurate crystalline structures, the Landau and Lifshitz conditions must be satisfied. For transitions to incommensurate structures, the Landau and ``weak Lifshitz'' conditions must be satisfied. The irreducible representations of each of the 230 crystallographic space groups that violate these conditions are listed.