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

TL;DR

This study explores the low-temperature critical behavior of 2D RP^{N-1} models, revealing a new universality class distinct from the O(N) models through large-scale simulations for N=3 and N=4.

Contribution

It demonstrates the existence of a new universality class for 2D RP^{N-1} models, different from the well-known O(N) universality class, based on extensive numerical simulations.

Findings

All models studied share the same finite-size scaling behavior.

The FSS curves differ from those of the 2D O(3) sigma model.

Results support a distinct RP^{N-1} universality class for N=3 and N=4.

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.