Two-dimensional power-law Debye model
= Two-dimensional power-law Debye model
For two polarizations, $n$ atoms in area $A$, and $\omega=C|k|^\alpha$, mode counting gives
$$
\omega_D=C\left(\frac{4\pi n}{A}\right)^{\alpha/2}.
$$
At low temperature its energy scales as $T^{1+2/\alpha}$ and its constant-volume heat capacity as $T^{2/\alpha}$.