The role of the twinning group of a domain pair in tensor distinction of domain states

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Abstract
As it has been recently shown, the appropriate definition of equivalent domain pairs, i.e., pairs exhibiting similar distinction, is that of the permutational equivalence. This equivalence uses the fact that a generic set of domain states can be assigned to a domain pair. The symmetry of the generic set of a pair, called the twinning group of a pair, then expresses the mutual relationship between two states of the pair. We show that the twinning group plays an indispensable role in domain distinction analysis. We focus on the following items: a) The relationship between the twinning group of a domain pair and secondary order parameters, and two kinds of invariants of the respective permutational class of pairs. b) The use of the twinning group for derivation of which properties change only the sign when switching from one state of the pair to the other state, and which coincide in both the states. Such characteristics are identified by means of sign-switching groups and stabilizing groups. An illustrative example of a sequence of successive phase transitions similar to the sequences in Fe-I, Co-Cl and Fe-Br boracites is given.