  We reconsider the formation of (global) cosmic strings during and after
preheating by calculating the dynamics of a scalar field on both two- and
three- dimensional lattices. We have found that there is little differences
between the results in two and three dimensions about the dynamics of
fluctuations, at least, during preheating. Practically, it is difficult to
determine whether long cosmic strings which may affect the later evolution of
the universe could ever be produced from the results of simulations on
three-dimensional lattices with smaller box sizes than the horizon. Therefore,
using two-dimensional lattices with large box size, we have found that cosmic
strings with the breaking scale 0\eta \sim 10^{16} GeV are produced for broad
range of parameter space in \eta, while for higher breaking scales (\eta \sim
3\times 10^{16} GeV), their production depends crucially on the value of the
breaking scale \eta in our simulations.
