Transition of Structure and Phase as a Condensation of Excitations

Abstract

The energy of the soft mode associated with a structural transition in a solid decreases as |T−T_c|^1⁄3 as the temperature T approaches the critical temperature T_c, which is identical to the real transition temperature if the transition is of the continuous second order. In a liquid-solid transition, an excitation with a nonvanishing momentum will become soft to finally result in the appearance of a periodic structure as the temperature approaches the transition point T_LS from above if the cause to yield the metastable characteristic of the liquid phase does not affect the dynamics of the softening very much. The energy of the excitation decreases as |T−T_c|^1⁄3 for the temperature decreasing toward a critical temperature T_c which is always less than the real transition temperature T_LS.