Theory of a ContinuousHc2Normal-to-Superconducting Transition

I study the $H_{c2\mathrm{}}$ transition within the Ginzburg-Landau model, with $m$-component order parameter ${\psi }_i$. I find a renormalized fixed point free energy, exact in $m\to \infty$ limit, suggestive of a second-order transition in contrast to the general belief of a first-order transition. The thermal fluctuations for $H\ne 0$ force one to consider an infinite set of marginally relevant operators for $d<\mathrm{}{d}_{\mathrm{uc}}=6\mathrm{}$. I find $d_{\mathrm{lc}}=4\mathrm{}$, predicting that the off-diagonal long-range order does not survive thermal fluctuations in $d=2,3\mathrm{}$. The result is a solution to a critical fixed point that was found to be inaccessible within $\epsilon =6-d$ expansion, previously considered by Brezin, Nelson, and Thiaville [Phys. Rev. B 31, 7124 (1985)], and was interpreted as a first-order transition.