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Dispersion refers to the frequency dependence of the properties of a wave.

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Dispersion of ferromagnetic ($E\propto k^2$) and antiferromagnetic ($E\propto k$) spin wave

The dispersion of ferromagnetic spin wave at low energy is $E\propto k^2$, while $E\propto k$ for antiferromagnetic case. Is there a simple/physical argument (such as symmetry) for these results? … Moreover, in a generic system with spontaneous continuous symmetry breaking, what determines the value of $n$ in the low energy dispersion $E\propto k^n$ of the Goldstone mode? …
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