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We simulate the formation and the evolution of global strings taking intoaccount the expansion of the universe and the concomitant change of theeffective potential, that is, the change from the restoration stage of theglobal {\it U}(1)-symmetry to the broken stage. Starting from the thermalequilibrium state, we run simulations for 100 sets of different initialconditions in 2+1 dimensions. As a result, we find deviation from scaleinvariance. This is because the energy loss mechanism is pair annihilationrather than intercommutation, so that a string and an anti-string attract eachother under a logarithmic potential.Comment: 17 pages, uuencode, gzipped tar file including LaTeX text and 7  postscript figures. Some statements are change

Numerical Analysis of the Formation and Evolution of Global Strings in 2+1 Dimensions