Statistical Theory, Soft Modes, And Phase Transitions
In order to acquire a simple physical picture of the dynamic mechanism of a phase transition it is necessary to use the simplest of many-body approximations. It is instructive, in particular, to study the mean-field response of the model system to a time-dependent applied field. In this way, one can obtain considerable insight into the nature of the collective excitations and into the relationship between the static aspects of a phase transition and the occurrence of temperature-dependent (that is, soft) modes and of critical fluctuations. This chapter discusses the static aspects of mean-field theory and the nature of the static singularities which accompany second-order phase transitions. Mean-field dynamics are then described in terms of deviations from the equilibrium mean-field state. Correlated effective-field theory, the quasi-harmonic limit and self-consistent phonons, the deep double-well limit and the Ising model, and the pseudo-spin formalism and tunnel mode are also considered.
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