Critical phenomena in nonlinear sigma models

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 a t 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 critica l phenomena found by Choptuik. (C) 2000 American Institute of Physics. [S00 22-2488(00)04908-2].