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

Abstract

I provide evidence that the 2D $R{P}^{N-1}$ model for $N\ge 3$ is equivalent to the $O(N)$-invariant non-linear $\sigma$-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 $R{P}^{N-1}$ 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 $R{P}^{N-1}$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 $R{P}^{N-1}$ and $O(N)$ models share a unique universality class.

14 pages (latex) + 1 figure (Postscript) ,uuencoded

References in corpus (2)

• New Universality Classes for Two-Dimensional $\sigma$-Models
• The XY Model and the Three-state Antiferromagnetic Potts model in Three Dimensions: Critical Properties from Fluctuating Boundary Conditions

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