Comparison of strong-coupling free-energy functionals for superfluid $^{3}{\rm He}$

Strong-coupling corrections to weak-coupling BCS theory have long been known to determine the equilibrium phase diagram of bulk superfluid $^{3}{\rm He}$. Recently Wiman and Sauls demonstrated the importance of strong-coupling corrections for phase diagrams of superfluid $^{3}{\rm He}$ in confined geometries, and introduced a computationally tractable extension of the strong-coupling Ginzburg-Landau free-energy as an alternative to the exact (through order $(T_c/T_F)^3)$ strong-coupling free-energy functional.\footnote{J.J. Wiman and J.A. Sauls, Phys. Rev. B {\bf 92}, 144515 (2015)} We will discuss the accuracy and range of applicability of the Wiman-Sauls functional using comparisons to calculations with the full strong-coupling theory.\footnote{J.W. Serene and D. Rainer, Phys. Rep. {\bf 101}, 221 (1983)}