Critical Phenomena in Nonlinear Sigma Models

@article{Liebling1999CriticalPI,
  title={Critical Phenomena in Nonlinear Sigma Models},
  author={Steven L. Liebling and Eric W. Hirschmann and James Isenberg},
  journal={Journal of Mathematical Physics},
  year={1999},
  volume={41},
  pages={5691-5700}
}
We consider solutions to the nonlinear sigma model (wave maps) with target space S3 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. 

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