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

Y. Meurice
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Abstract

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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Y. Meurice. 2002-09-04. Complex singularities of the critical potential in the large-N limit. https://doi.org/10.1103/physrevd.67.025006

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