= Solution
Write $D=\rho_s/s$, so $\omega_k=Dk^2$, and take $\Gamma_k=\gamma|k|$. The small-wavenumber <static structure factor> behaves as
$$
S(k)\propto
\frac{TD\gamma}{|k|(\gamma^2+D^2k^2)^2}
\sim\frac{TD}{\gamma^3|k|}.
$$
The spatial <Fourier transform> of $|k|^{-1}$ in $d$ dimensions scales as $|x|^{1-d}$. Thus
$$
C(x)\sim \text{constant}\times |x|^{1-d},
$$
and in three dimensions $C(x)\sim |x|^{-2}$. Since this <two-point correlation function> tends to zero rather than to a nonzero constant at large separation, it is incompatible with true long-range ferromagnetic order and hence with <spontaneous symmetry breaking> at this higher temperature.
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