  The formation of vortex loops (global cosmic strings) in an O(2) linear sigma
model in three spatial dimensions is analyzed numerically. For over-damped
Langevin dynamics we find that defect production is suppressed by an
interaction between correlated domains that reduces the effective spatial
variation of the phase of the order field. The degree of suppression is
sensitive to the quench rate. A detailed description of the numerical methods
used to analyze the model is also reported.
