Phase transitions, soft modes, and critical fluctuations

This paper gives an introductory review of the field of phase transitions. The first part contains a general discussion of the dynamical mechanism of phase transitions. The interactions between the particles are shown to yield a feedback effect in the collective response of the system to small external perturbations. This feedback provides the mechanism which can give rise to instabilities for certain critical values of the external parameters. It is pointed out how the static aspects of the instability (characterized by a singularity in the static response function) are intimately related to dynamic aspects, namely the occurrence of soft collective modes and of critical fluctuations. In the second part, the general picture is illustrated by a number of specific examples. Experimental results on soft mode behavior and critical fluctuations are shown for ferromagnetic, antiferromagnetic, ferroelectric, and structural phase transitions. It is further demonstrated that the existence of critical fluctuations near a phase transition gives rise to anomalous behavior of various physical properties of the system. Finally, some problems are indicated which arise in connection with instabilities occurring in nonequilibrium systems.