Group theory of the Landau — Thermodynamic theory of continuous phase transitions in crystals

Abstract

A review is given of group-theory related aspects of the Landau-Thermodynamic Theory of continuous phase transitions in crystals. The review discusses developments of the theory during several time intervals. First interval: the 25 years (1937–62) after the theory was presented; Second interval (1962-77) covers the recent 15 years; Third interval (1977- ) presents some possible directions for work in the future. Thus the first 40 years of this theory were characterized inter alia by elaborations and applications of the group theory aspects of the problem which Landau examined: Given a system with group G; What groups G → G′,... may be achieved by continuous transitions i.e. G → G′,...? What order parameters are consistent with transitions G → G′, or G → G′, ...?