The equivalence between the Lawrence-Doniaeh model for films of extrem
e type-II layered superconductors and a generalization of the back-sca
ttering model for spin-(1/2) electrons in one dimension is demonstrate
d. This fermion analogy is then exploited to obtain an anomalous H-par
allel to(-1) tail for the parallel equilibrium magnetization of the mi
nimal double-layer case in the limit of high parallel magnetic fields
H-parallel to for temperatures in the critical regime.