  The density of extended topological defects created during symmetry-breaking
phase transitions depends on the ratio between the correlation length in the
symmetric phase near $T_c$ and the winding length of the defects as determined
by the momentaneous effective action after a typical relaxation time.
Conservation of winding number in numerical simulations requires a suitable
embedding of the field variables and the appropriate geometrical implementation
of the winding density on the discrete lattice. We define a modified Kibble
limit for the square lattice and obtain defect densities as functions of
winding lengths in O(2) and O(3) models. The latter allows to observe formation
of disoriented aligned domains within the easy plane. Their extent is severely
limited by the momentaneous defect density during the course of the quench.
