Defect-induced condensation and the central peak at elastic phase transitions

Static and dynamical properties of elastic phase transitions under the influence of short–range defects, which locally increase the transition temperature, are investigated. Our approach is based on a Ginzburg–Landau theory for three–dimensional crystals with one–, two– or three–dimensional soft sectors, respectively. Systems with a finite concentration nD of quenched, randomly placed defects display a phase transition at a temperature T_c(nD), which can be considerably above the transition temperature T⁰_c of the pure system. The phonon correlation function is calculated in single–site approximation. For T > T_c(nD) a dynamical central peak appears; upon approaching T_c(nD), its height diverges and its width vanishes. Using an appropriate self–consistent method, we calculate the spatially inhomogeneous order parameter, the free energy and the specific heat, as well as the dynamical correlation function in the ordered phase. The dynamical central peak disappears again as the temperatur is lowered below T_c(nD). The inhomogeneous order parameter causes a static central peak in the scattering cross section, with a finite k width depending on the orientation of the external wave vector k relative to the soft sector. The jump in the specific heat at the transition temperatur of the pure system is smeared out by the influence of the defects, leading to a distinct maximum instead. In addition, there emerges a tiny discontinuity of the specific heat at T_c(nD). We also discuss the range of validity of the mean–field approach, and provide a more realistic estimate for the transition temperature.