The normal-to-planar superfluid transition in Helium 3

TL;DR

This paper investigates the continuous nature of the superfluid transition in Helium-3 from the normal to the planar phase, using advanced RG analysis to identify a stable fixed point and compute critical exponents.

Contribution

It provides a detailed RG analysis of the Helium-3 superfluid transition, predicting its continuous nature and calculating critical exponents using high-order perturbative schemes.

Findings

Presence of a stable fixed point indicating a continuous transition

Estimated specific-heat exponent α = 0.20(15)

Magnetic susceptibility exponent γ_H = -0.34(5)

Abstract

We study the nature of the Helium-3 superfluid transition from the normal to the planar phase, which is expected to be stabilized by the dipolar interactions. We determine the RG flow of the corresponding Landau-Ginzburg-Wilson theory by exploiting two fixed-dimension perturbative schemes: the massive zero-momentum scheme and the minimal-subtraction scheme without $\epsilon$ expansion. The analysis of the corresponding six-loop and five-loop series shows the presence of a stable fixed point in the relevant coupling region. Therefore, we predict the transition to be continuous. We also compute critical exponents. The specific-heat exponent $\alpha$ is estimated as $\alpha = 0.20(15)$, while the magnetic susceptibility and magnetization exponents $\gamma_H$ and $\beta_H$ for Helium 3 are $\gamma_H = -0.34(5)$, $\beta_H = 1.07(9)$.