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arXiv · hep-lat/9507008

O(N) and RP^{N-1} Models in Two Dimensions

Martin Hasenbusch
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Abstract

I provide evidence that the 2D $RP^{N-1}$ model for $N \ge 3$ is equivalent to the $O(N)$-invariant non-linear $σ$-model in the continuum limit. To this end, I mainly study particular versions of the models, to be called constraint models. I prove that the constraint $RP^{N-1}$ and $O(N)$ models are equivalent for sufficiently weak coupling. Numerical results for their step-scaling function of the running coupling $\bar{g}^2= m(L) L$ are presented. The data confirm that the constraint $O(N)$ model is in the samei universality class as the $O(N)$ model with standard action. I show that the differences in the finite size scaling curves of $RP^{N-1}$i and $O(N)$ models observed by Caracciolo et al. can be explained as a boundary effect. It is concluded, in contrast to Caracciolo et al., that $RP^{N-1}$ and $O(N)$ models share a unique universality class.

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Martin Hasenbusch. 1995-07-07. O(N) and RP^{N-1} Models in Two Dimensions. https://doi.org/10.1103/physrevd.53.3445

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