Nonuniformity of the $1/N$ Expansion for Two-Dimensional $O(N)$ Models

A. Patrascioiu; E. Seiler

doi:10.1016/0550-3213(95)00145-i

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arXiv · hep-lat/9407003

Nonuniformity of the $1/N$ Expansion for Two-Dimensional $O(N)$ Models

A. Patrascioiu·E. Seiler

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Abstract

We point out that the $1/N$ expansion, which is widely invoked to infer properties of the $2D$ $O(N)$ models, is nonuniform in the temperature, i.e. with decreasing temperature the $1/N$ expansion truncated at a fixed order deviates more and more from the true answer. This fact precludes the use of the expansion to deduce low temperature properties such as asymptotic scaling for those models. By contrast, in the $1D$ $O(N)$ chains, there are no signs of such a nonuniformity.

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A. Patrascioiu, E. Seiler. 1994-07-05. Nonuniformity of the $1/N$ Expansion for Two-Dimensional $O(N)$ Models. https://doi.org/10.1016/0550-3213(95)00145-i

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