Critical Phenomena in Nonlinear Sigma Models

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.

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

References in corpus (3)

• Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere
• Critical Phenomena Inside Global Monopoles
• Are there static texture?

Cited by in corpus (12)

• Critical phenomena in gravitational collapse
• Critical phenomena in gravitational collapse (Physics Reports)
• Numerical Approaches to Spacetime Singularities
• The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive Mesh Refinement
• On blowup for Yang-Mills fields
• Type II Critical Collapse of a Self-Gravitating Nonlinear $\sigma$-Model
• On stable self-similar blow up for equivariant wave maps: The linearized problem
• Singularity Formation in 2+1 Wave Maps
• A New Transition between Discrete and Continuous Self-Similarity in Critical Gravitational Collapse
• The Nonlinear Sigma Model With Distributed Adaptive Mesh Refinement
• Threshold of Singularity Formation in the Semilinear Wave Equation
• Maxwell-dilaton dynamics