Renormalization Group Studies of Statics and Dynamics of Liquid Crystal Phase Transitions
Liquid crystals exhibit a wide variety of continuous phase transitions between different mesophases. Due to divergent critical fluctuations, simple theoretical descriptions such as mean field theory and perturbation theory break down in the vicinity of these transitions. Static and dynamic behavior in the critical region may be analyzed by using Renormalization Group (RG) methods. The starting point of a RG calculation of the static critical behavior is the Ginzburg-Landau (GL) free energy expressed as a functional of the order parameter field. In some cases, due to symmetry or other considerations, terms coupling the order parameter to other non-ordering fields may have to be included in the GL functional. Standard methods1 are used to obtain the RG recursion relations for the coupling constants appearing in the GL functional. Information about the critical properties is obtained from an analysis of these recursion relations. Such calculations have been carried out for several liquid crystal transitions, including the nematic to smectic A transition2–5, the nematic-smectic A-smectic C multicritical point6, various hexatic transitions in two and three dimensions7–9 and transitions between different smectic A phases10–11. Results obtained from these studies are reviewed in Section 2.
KeywordsRenormalization Group Critical Behavior Continuous Phase Transition Renormalization Group Method Renormalization Group Transformation
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