Abstract
Fröhlich has shown that a one-dimensional metal, at absolute zero, can exhibit certain of the properties of a superconductor when the interaction between the lattice vibrations and the electrons is sufficiently strong. The self-consistent method used by him is extended to finite temperatures, and the specific heat is calculated. It is shown that the model exhibits a second-order transition at a temperature which is related to the magnitude of the coupling constant. The approximations demand a coupling constant which is much larger than that of any real metal.
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