Phase Transitions and Critical Phenomena

Abstract

Regimes of behavior in which a given macroscopic variable of thermodynamic significance changes from being zero in the disordered phase to a nonzero value in the ordered phase are separated by phase transitions. A disordered liquid crystallizing to form a solid crystal of long-range order is another example of a phase transition that breaks the continuous translational symmetry because each point in a crystal does not have the same properties as those observed in a fluid. The concept of the order parameter was introduced by Landau to describe phase transitions. This theory neglects fluctuations, implying that the order parameter is assumed constant in time and space. Therefore, the Landau theory is a mean-field theory. Consequently, the discrete phase transition point disappears, and the transition is “smoothed out.” The chapter shows that instead of a sharp discontinuity in the specific heat, there is an anomalous spread over a temperature range.