  We show how to obtain the O(N) non-linear sigma model in two dimensions as a
strong coupling limit of the corresponding linear sigma model. In taking the
strong coupling limit, the squared mass parameter must be given a specific
coupling dependence that assures the finiteness of the physical mass scale. The
relation discussed in this paper, which applies to the renormalized theories as
opposed to the regularized theories, is an example of a general relation
between the linear and non-linear models in two and three dimensions.
