totally uncorrelated. Essentially, the chiral field defines a smooth map from the region covered by the domains into the manifold ${\cal M}$. The image of this map is actually a smooth and connected patch in the manifold ${\cal M}$. Smoothness of this patch is enforced by the condition that the chiral field must smoothly interpolate in-between any two adjacent domains. When the chiral field relaxes, this patch deforms as its portions slide down to the global minimum. It is quite conceivable that this type of evolution of the chiral field leads to a pion condensate pointing in a direction which is in some way the average direction defined by the patch. It is thus not clear that small individual domains imply no pion condensate in large regions.

We will not, however, pursue this line of argument since $\epsilon_2 = 0$ is unnecessarily restrictive. Rather, we will show that a non-zero value of $\epsilon_2$ leads to the existence of large domains in a very natural manner.

As discussed in sect. 2, non-zero values of $\epsilon_2$ lead to the existence of domain walls if the inequality $\epsilon_1
< f_\pi \epsilon_2$ is satisfied. \[If not then there is no qualitative difference between this 