Magnetic Scaling in Superconductors

Abstract

The Ginzburg-Landau-Wilson superconductor in a magnetic field $B$ is considered in the approximation that magnetic-field fluctuations are neglected. A formulation of perturbation theory is presented in which multiloop calculations fully retaining all Landau levels are tractable. A 2-loop calculation shows that, near the zero-field critical point, the singular part of the free energy scales as ${F}_{\mathrm{sing}}\ensuremath{\approx}\phantom{\rule{0ex}{0ex}}|t{|}^{2\ensuremath{-}\ensuremath{\alpha}}F(B|t{|}^{\ensuremath{-}2\ensuremath{\nu}})$, where $\ensuremath{\nu}$ is the coherence-length exponent---a result which has hitherto been assumed on purely dimensional grounds.