Critical Phenomena in Nonlinear Sigma Models

Details Critical Phenomena in Nonlinear Sigma Models Critical Phenomena in Nonlinear Sigma Models

1999-11-13

arxiv.org/abs/math-ph/9911020v2

J.Math.Phys. 41 (2000) 5691-5700

Physics

Mathematical Physics

7 pages, 4 figures; a couple small corrections; a revised discussion of the role of the static solution; main conclusions unal

Scientific paper

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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