= Order-parameter phase
{title2=$\theta=\arg(m_x+im_y)$}
For a two-component <order parameter> of nonzero magnitude, write $m_x+im_y=\bar m e^{i\theta}$. Its phase is the orientation angle modulo $2\pi$, not a <thermodynamic phase> such as an ordered or disordered state. A global continuous <symmetry> rotates this angle uniformly; <spin waves> are smooth spatial changes, while a <phase vortex> has nonzero winding around an excluded core. At a zero of the magnitude the angle is undefined, allowing the topology of an orientation field to change.
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