The normal-to-planar superfluid transition in Helium 3

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 $ϵ$ 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 ${\gamma }_H=-0.34(5)$, ${\beta }_H=1.07(9)$.

Comments: 19 pages, 4 figs