  We examine the vacuum overlap formula for the two-dimensional SU(2)
Wess-Zumino term in lattice regularization. Perturbatively it reproduces the
Wess-Zumino term correctly in the continuum limit and yields the IR fixed point
in the beta function of the chiral model. Nonperturbatively it shows a sharp
Gaussian distribution for the SU(2) chiral field configurations in the scaling
region, where smooth configurations dominate even in the symmetric phase due to
asymptotic freedom. Crossover is sharp from the strong coupling region where
the Wess-Zumino term fluctuates hard and the species doublers' contribution is
suspected to affect it.
