text: Irreducible representations Landau expanded his theory to consider the restraints that it imposes on the symmetries before and after a transition of second order. They need to comply with a number of requirements:
  The distorted (or ordered) symmetry needs to be a subgroup of the higher one.
  The order parameter that embodies the distortion needs to transform as a single irreducible representation (irrep) of the parent symmetry
  The  irrep should not contain a third order invariant
  If the irrep allows for more than one fourth order invariant, the resulting symmetry minimizes a linear combination of these invariants
  In the latter case more than one daughter structure should be reacheable through a continuous transition. A good example of this are the structure of MnP (space group Cmca) and the low temperature structure of NbS (space group P63mc). They are both daughters of the NiAs-structure and their distortions transform according to the same irrep of that spacegroup.
  Applied fields
  In many systems, one can consider a perturbing field  that couples linearly to the order parameter. For example, in the case of a classical dipole moment , the energy of the dipole-field system is . In the general case, one can assume an energy shift of  due to the coupling of the order parameter to the applied field , and the Landau free energy will change as a result:
  In this case, the minimization condition is