Asymptotic low-temperature behavior of two-dimensional RP${}^{N-1}$ models

Abstract

We investigate the low-temperature behavior of two-dimensional (2D) RP${}^{N-1}$ models, characterized by a global O($N$) symmetry and a local ${\mathbb{Z}}_2$ symmetry. For $N=3$ we perform large-scale simulations of four different 2D lattice models: two standard lattice models and two different constrained models. We also consider a constrained mixed O(3)-RP${}^2$ model for values of the parameters such that vector correlations are always disordered. We find that all these models show the same finite-size scaling (FSS) behavior, and therefore belong to the same universality class. However, these FSS curves differ from those computed in the 2D O(3) $\sigma$ model, suggesting the existence of a distinct 2D RP${}^2$ universality class. We also performed simulations for $N=4$, and the corresponding FSS results also support the existence of an RP${}^3$ universality class, different from the O(4) one.

Comments: 10 pages, 9 eps figures, comments added