Critical behavior of three-dimensional magnets with complicated ordering from three-loop renormalization-group expansions

TL;DR

This paper investigates the critical behavior of three-dimensional antiferromagnets with complex order parameters using three-loop renormalization-group calculations, revealing an anisotropic fixed point with exponents similar to the XY model.

Contribution

The study provides a detailed three-loop RG analysis of 3D magnets with complicated ordering, identifying a stable fixed point and estimating critical exponents.

Findings

Existence of an anisotropic stable fixed point for N > 1

Critical exponents close to those of the XY model

RG functions calculated up to three-loop order and resummed

Abstract

The critical behavior of a model describing phase transitions in 3D antiferromagnets with 2N-component real order parameters is studied within the renormalization-group (RG) approach. The RG functions are calculated in the three-loop order and resummed by the generalized Pade-Borel procedure preserving the specific symmetry properties of the model. An anisotropic stable fixed point is found to exist in the RG flow diagram for N > 1 and lies near the Bose fixed point; corresponding critical exponents are close to those of the XY model. The accuracy of the results obtained is discussed and estimated.