  The equivalence between the Lawrence-Doniach model for films of extreme
type-II layered superconductors and a generalization of the back-scattering
model for spin-1/2 electrons in one dimension is demonstrated. This fermion
analogy is then exploited to obtain an anomalous $H_{\parallel}^{-1}$ tail for
the parallel equilibrium magnetization of the minimal double layer case in the
limit of high parallel magnetic fields $H_{\parallel}$ for temperatures in the
critical regime.
