Critical Phenomena in Nonlinear Sigma Models
Mathematical Physics
2015-06-26 v2 General Relativity and Quantum Cosmology
High Energy Physics - Phenomenology
Analysis of PDEs
math.MP
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.
Cite
@article{arxiv.math-ph/9911020,
title = {Critical Phenomena in Nonlinear Sigma Models},
author = {Steven L. Liebling and Eric W. Hirschmann and James Isenberg},
journal= {arXiv preprint arXiv:math-ph/9911020},
year = {2015}
}
Comments
7 pages, 4 figures; a couple small corrections; a revised discussion of the role of the static solution; main conclusions unaltered