Phase Transitions

Abstract

A gas whose equation of state is described by the Boyle-Charles law and a paramagnetic substance which obeys Curie’s law are examples of so-called ideal systems. These systems are composed of elements with negligible interactions and the treatment of these systems can be reduced essentially to that of a single element. The harmonically vibrating lattices have strong interactions among particles, but they are ideal systems in view of the existence of normal modes or phonons. In contrast to these ideal systems, systems which are by no means reducible to ideal systems exist and thus have strong interactions among constituent elements which can never be ignored. They are sometimes called cooperative systems and exhibit, among other things, a cooperative phenomenon called a phase transition. For example, a gas condenses to the liquid state by compression or by cooling, and a paramagnetic substance becomes ferromagnetic by cooling below the Curie temperature. The ideal Bose gas undergoes a Bose condensation, because it can be regarded effectively as a cooperative system having attractive interactions among atoms by virtue of the symmetry of the wave function. Through a phase transition, a substance acquires a new structure or a new property which is absent before the phase transition. Sometimes the biological function of a biomaterial can be regarded as a result of a phase transition.