Density of strings formed at a second-order cosmological phase transition

We discuss the problem of estimating the characteristic length scale $\xi_{\rm s}$, and hence the initial density, of a system of cosmic strings formed at a continuous, second-order phase transition in the early universe. In particular, we examine the roles of the correlation length (or string width) $\xi_{\rm c}$ and the Ginzburg length $\xi_{\rm G}$ which defines the ``fuzziness'' of long strings. We argue that strings acquire a clear identity only once $\xi_{\rm s}$ exceeds both $\xi_{\rm c}$ and $\xi_{\rm G}$, and estimate its magnitude at that time.