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∥−1 tail for the parallel equilibrium magnetization of the minimal double-layer case in the limit of high parallel magnetic fields H∥ for temperatures in the critical regime.