Analysis of Landau Potentials for Six-Dimensional Order Parameters and Realization of Non-Maximal Isotropy Subgroups

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Abstract
We have classified continuous phase transitions in physical systems whose order parameter transforms as a six-dimensional representation of a space group. The Landau potential is minimized using Kim's geometrical method and using a table of isotropy subgroups obtained by Stokes and Hatch. The procedure is illustrated in four examples. The complete lists of stable phases for these examples are presented along with the corresponding regions in coupling constant space for each stable phase. Many interesting counter-examples to the maximality conjectures are found.