Symmetry breaking background

The finite-temperature field theory has been the most popular approach to equilibrium phase transitions (L. Dolan et.al., 1974). The effective potential of quantum fluctuations around a classical background provides a convenient tool to describe phase transitions. The symmetry breaking or restoration mechanism can be illustrated by a scalar field model with broken symmetry... 

Fig. 12. Schematic of BaTi03 NMR results, (a) Cubic structure (b) displacive model with the tetragonal distortion (c) order-disorder model with eight sites along the body diagonals (d) HT paraelectric phase T> Tc. Up spectra with the satellite background down second moment as a function of rotation in the HT paraelectric phase T>TC indicating a tetragonal local symmetry breaking.

The individual satelhte transitions cannot be resolved above Tc due to exchange of Ti ions between off-center sites. Discrimination between tetragonal, orthorhombic, and rhombohedral breaking of the cubic symmetry can be obtained from the angular dependence of the second moments M2 of the satelhte background [9]. 

Chiral liquid crystals belong to a wide class of soft condensed phases. The director field in the ground state of chiral phases is nonuniform because molecular interactions lack inversion symmetry. Among the broad variety of spatially distorted structures the simplest one is the cholesteric phase in which the director n is twisted into a helix. The spatial scale of background deformations, e.g., the pitch p of the helix, is normally much larger than the molecular size ( > 0.1 pm) since the interactions that break the inversion symmetry are weak. 

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