  We consider solutions to the nonlinear sigma model (wave maps) with target
space S^3 and base space 3+1 Minkowski space, and we find critical behavior
separating singular solutions from nonsingular solutions. For families of
solutions with localized spatial support a self-similar solution is found at
the boundary. For other families, we find that a static solution appears to sit
at the boundary. This behavior is compared to the black hole critical phenomena
found by Choptuik.
