Cosmic string formation and the power spectrum of field configurations

We examine the statistical properties of defects formed by the breaking of a U(1) symmetry when the Higgs field has a power spectrum $P(k) \propto k^n$. We find a marked dependence of the amount of infinite string on the spectral index $n$ and empirically identify an analytic form for this quantity. We also confirm that this result is robust to changes in the definition of infinite string. It is possible that this result could account for the apparent absence of infinite string in recent lattice-free simulations.