Scaling behavior and phases of nonlinear sigma model on real Stiefel manifolds near two dimensions

TL;DR

This paper investigates the phase structure and critical behavior of a quasi-two-dimensional nonlinear sigma model on real Stiefel manifolds, revealing a tetracritical point with specific critical exponents.

Contribution

It derives one-loop RG equations for the model with anisotropic metrics and identifies conditions for the existence of a tetracritical point in the phase diagram.

Findings

Existence of a tetracritical point with four phases

Critical exponents evaluated and compared with simpler cases

RG trajectories analyzed for different metric structures

Abstract

For a quasi-two-dimensional nonlinear sigma model on the real Stiefel manifolds with a generalized (anisotropic) metric, the equations of a two-charge renormalization group (RG) for the homothety and anisotropy of the metric as effective couplings are obtained in a one-loop approximation. Normal coordinates and the curvature tensor are exploited for the renormalization of the metric. The RG trajectories are investigated and the presence of a fixed point common to four critical lines or four phases (tetracritical point) in the general case, or its absence in the case of an Abelian structure group, is established. For the tetracritical point, the critical exponents are evaluated and compared with those known earlier for a simpler particular case.