The Large-N Limit of PT-Symmetric O(N) Models

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dc.creatorNishimura, Hiromichi
dc.creatorOgilvie, Michael
dc.date2008-10-21
dc.date.accessioned2026-07-07T12:15:53Z
dc.date.available2026-07-07T12:15:53Z
dc.descriptionWe study a $PT$-symmetric quantum mechanical model with an O(N)-symmetric potential of the form $m^{2}\vec{x}^{2}/2-g(\vec{x}^{2})^{2}/N$ 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 $m^{2}/g^{2/3}$, given by $3\cdot2^{1/3}$.
dc.description7 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0810.3910
dc.identifierhttp://arxiv.org/abs/0810.3910
dc.identifierJ.Phys.A42:022002,2009
dc.identifierdoi:10.1088/1751-8113/42/2/022002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/211629
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleThe Large-N Limit of PT-Symmetric O(N) Models
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