Symmetry-breaking field

The prefactor L in Eq. (36) is understood from the normalization condition, i d Pj ,( ) = 1, which must hold at all temperatures. From Eq. (36) one immediately obtains finite-size scaling relations for the order parameter < >T and ordering susceptibility by taking suitable moments of the distribution (note PJl ) is symmetric around ijf — O in the absence of symmetry-breaking fields and thus < > = 0) ... 

Because there is no symmetry-breaking field like a concentration gradient, it is equally likely for a bacterium to move off in one direction as another. Therefore P( ) should not depend on the direction of V but only on its magnitude V. Thus the angular integrations can be carried through, yielding... 

Higgs field The symmetry-breaking field associated with a Higgs boson. The Higgs... 

Fig. 28. Reduction of the squared AF moment in UPt3 with hydrostatic pressure p (above), it vanishes at a critical pressure of — 3.8 kbar. Simultaneously the SC Tq splitting is reduced and also vanishes at pc staying zero for larger pressures (Hayden et al., 1992). This supports the idea that a two-fold degenerate SC order parameter (e.g., E2m) is split by an AF symmetry breaking field according to eqs. (69), (70).

Second harmonic generation from surfaces has been shown to be a powerful probe of surface interactions [97], which can yield information about the structure and alignment of liquid crystal molecules on surfaces and at interfaces [98], The role of the interface is similar to that of the dc electric field in electric-field-induced SHG, that is, to provide a symmetry-breaking field the direction of which is defined by the surface normal. 

When an external, symmetry breaking field is applied perpendicular to the director of a nematic liquid crystal, confined between two orienting surfaces, the lowest order fluctuation mode undergoes a softening and... 

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