Complex singularities of the critical potential in the large-N limit

Details Complex singularities of the critical potential in the large-N limit Complex singularities of the critical potential in the large-N limit

2002-08-25

arxiv.org/abs/hep-th/0208181v2

Phys.Rev. D67 (2003) 025006

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, 9 figures, uses revtex

Scientific paper

10.1103/PhysRevD.67.025006

We show with two numerical examples that the conventional expansion in powers of the field for the critical potential of 3-dimensional O(N) models in the large-N limit, does not converge for values of phi^2 larger than some critical value. This can be explained by the existence of conjugated branch points in the complex phi^2 plane. Pade approximants [L+3/L] for the critical potential apparently converge at large phi^2. This allows high-precision calculation of the fixed point in a more suitable set of coordinates. We argue that the singularities are generic and not an artifact of the large-N limit. We show that ignoring these singularities may lead to inaccurate approximations.

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