String production as a result of thermal fluctuations

Based on the analysis of the free energies of topological defects, we develop further the study of phase transitions in field theory at finite temperature. In the case of strings we have shown how one can get, in the dilute-gas approximation, explicit expressions for the length of the string as well as the density contrast in terms of the free energy per unit length of the string. In the high-temperature limit one can get explicit expressions for all relevant quantities up to the one-loop approximation. When applied to the SO(10) model we get good phenomenological results. In particular we derive, in a simple manner, the scale-independent Zel'dovich spectrum with the right order of magnitude.