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Effective Field Approach to Phase Transitions And Some Applications to Ferroelectrics (World Scintific Lecture Notes in Physics)

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The effective field approach to a phase transition, used by Pierre Weiss at the beginning of this century to describe theoretically ferromagnetic transitions in iron, nickel, and cobalt, is the second oldest (surpassed in this respect only by Van der Waals theory of liquid-vapor transitions) and certainly the simplest approach to investigate cooperative phenomena of this kind. Early in the effort to describe satisfactorily the rich variety of physical phenomena accompanying a phase transition, it was realized that the role of fluctuations, introduced by Einstein in 1905 (the same year in which he introduced special relativity and the first successful explanation of the photoelectric effect), was crucial to investigate the subtleties of the behavior of systems undergoing phase changes at temperatures very close to the transition temperature. Of course, the concept of effective field, being an average or mean field, leaves out completely thermodynamic fluctuations. Nevertheless, the effective field approach gives in most cases a good qualitative description of the cooperative phenomena, and in some cases, ferroelectric transitions being an outstanding example, it even gives a fairly good quantitative description. It took some time for prominent theorists to realize that deviations of "classical" (effective field) behavior in ferroelectrics and dipolar ferromagnets should show up in the form of logarithmic corrections, which are very hard to detect experimentally.

This book begins by introducing the effective field approach, the simplest approach to phase transitions. It provides an intuitive approximation to the physics of such diverse phenomena as liquid-vapor transitions, ferromagnetism, superconductivity, order-disorder in alloys, ferroelectricity, superfluidity and ferroelasticity. The connection between the effective field approach and Landau's theory is stressed. The main coverage is devoted to specific applications of the effective field concept to ferroelectric systems, both hydrogen bonded ferroelectrics, like those in the TGS family, and oxide ferroelectrics, like pure and mixed perovskites.

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