Critical behavior of isotropic systems with strong dipole-dipole interaction from the functional renormalization group

TL;DR

This paper uses the functional renormalization group to compute critical exponents of 3D magnets with strong dipole interactions, revealing their proximity to the Heisenberg universality class.

Contribution

It identifies the Aharony fixed point governing such systems and computes its critical exponents nonperturbatively within the FRG framework.

Findings

Critical exponents are close to those of the Heisenberg O(3) class.

The Aharony fixed point is scale-invariant but not conformally invariant.

The analysis confirms the universality class proximity.

Abstract

We compute the critical exponents of three-dimensional magnets with strong dipole-dipole interactions using the functional renormalization group (FRG) within the local potential approximation including the wave function renormalization (LPA$^\prime$). The system is governed by the Aharony fixed point, which is scale-invariant but lacks conformal invariance. Our nonperturbative FRG analysis identifies this fixed point and determines its scaling behavior. The resulting critical exponents are found to be close to those of the Heisenberg $O(3)$ universality class, as computed within the same FRG/LPA$^\prime$ framework. This proximity confirms the distinct yet numerically similar nature of the two universality classes.