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Critical Phenomena in Nonlinear Sigma Models

Steven L. Liebling·Eric W. Hirschmann·James Isenberg
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Abstract

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.

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Steven L. Liebling, Eric W. Hirschmann, James Isenberg. 2000-06-01. Critical Phenomena in Nonlinear Sigma Models. https://doi.org/10.1063/1.533432

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