Phase transitions, critical phenomena, and instabilities

Transformations among many of the diverse states of matter arise from microscopic interactions involving very many (approximately 10(23)) constituent particles and result in dramatic changes in macroscopic properties. The values of some physical parameters vanish, while others approach infinity. These changes and their evolution are strikingly similar in systems as apparently different as liquids, magnets, superconductors, ferroelectrics, and liquid crystals, which suggests that there is an underlying unity to phase transition phenomena. The basis and extent of this unity are reviewed for many-body systems in equilibrium, and analogies with instability phenomena in systems far from equilibrium (such as lasers, fluid flows, and avalanche electronic devices) are pointed out.