Hiromichi Nishimura and Michael Ogilvie 2009 J. Phys. A: Math. Theor. 42 022002 doi:10.1088/1751-8113/42/2/022002
The large-N limit of PT-symmetric O(N) models
FREE ARTICLEHiromichi Nishimura and Michael Ogilvie
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We study a PT-symmetric quantum-mechanical model with an O(N)-symmetric potential of the form 
using its equivalent Hermitian form. Although the corresponding classical model has finite-energy trajectories that escape to infinity, the spectrum of the quantum theory is proven to consist only of bound states for all N. We show that the model has two distinct phases in the large-N limit, with different scaling behaviors as N goes to infinity. The two phases are separated by a first-order phase transition at a critical value of the dimensionless parameter m2/g2/3, given by 3 × 21/3.
- PACS
- MSC
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15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)
- Subjects
- Dates
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Issue 2 (16 January 2009)
Received 22 October 2008, in final form 16 November 2008
Published 4 December 2008
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The large-N limit of PT-symmetric O(N) models
Hiromichi Nishimura and Michael Ogilvie 2009 J. Phys. A: Math. Theor. 42 022002
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