Symmetry Restoring Modes and Soft Modes in Continuous Phase Transitions in Crystals

The mechanism which restores the symmetry broken by continuous (second order) phase transitions in crystals is discussed. It is a kind of extension of the concept of Goldstone's mode to the case of discrete broken symmetries. Relations between a symmetry restoring mode and a soft mode are given. It is shown that they are not necessarily identical, in particular if a soft mode is degenerate, the symmetry restoring mechanism gives rise to an additional mode centered at zero frequency. Qualitative behaviour of this mode near the critical temperature is derived using a specific model analogous to molecular rotation in liquids. It is essentially a reorientational diffusion motion originating from the anisotropic potential for the fluctuation of the eigenvectors of the soft mode. Phase transitions in several types of crystals are discussed from the symmetry restoring point of view.