= Order-parameter space
An <order-parameter space> is the set of allowed <equilibrium> values of an <order parameter> after accounting for the relevant <symmetry> breaking. When a <symmetry group> $G$ leaves a selected state invariant only under a subgroup $H$, the distinct symmetry-related states are often represented by the quotient $G/H$.
For a planar magnet with a fixed nonzero <magnetization> magnitude and free direction, the space is a circle. For a nematic orientation, opposite directions represent the same state, giving a different space. Its <topology> constrains possible <topological defects>; the physical identification of states matters as much as the number of coordinates.
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