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Statistical properties of the system of strings produced at a phase transition in the early universe are studied using a Monte Carlo simulation. The fractal dimension of the strings and the size distribution of closed loops are determined, and it is shown that infinite strings contribute about 80% to the total length of strings in the universe. The results are used to analyze the cosmological evolution of strings. Formation of domain walls and of walls bounded by strings is also discussed, and it is shown that in both cases the system is dominated by one infinite cluster of very complicated topology. The results of the simulations may also be of interest in condensed-matter systems where similar topological defects can be formed.
Vachaspati et al. (1984) studied this question.