Fermion Analogy for Layered Superconducting Films in Parallel Magnetic Field

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.