  Global, symmetry-breaking phase transitions in the early universe can
generate scaling seed networks which lead to metric perturbations. The acoustic
waves in the photon-baryon plasma sourced by these metric perturbations, when
Silk damped, generate spectral distortions of the cosmic microwave background
(CMB). In this work, the chemical potential distortion ($\mu$) due to scaling
seed networks is computed and the accompanying Compton $y$-type distortion is
estimated. The specific model of choice is the $O(N)$ nonlinear $\sigma$-model
for $N\gg 1$, but the results remain the same order of magnitude for other
scaling seeds. If CMB anisotropy constraints to the $O(N)$ model are saturated,
the resulting chemical potential distortion $\mu \lesssim 2\times 10^{-9}$.
