We have found a new mean field solution in the BCS theory of superconductivity. This unconventional solution indicates the existence of superconducting phase transitions of third order in thin films, or in bulk matter with a layered structure. The critical temperature increases with decreasing thickness of the layer, and does not exhibit the isotope effect. The electronic specific heat is a continuous function of temperature with a discontinuity in its derivative.
@article{arxiv.cond-mat/9906360,
title = {Third-order phase transition and superconductivity in thin films},
author = {Christofer Cronstrom and Milan Noga},
journal= {arXiv preprint arXiv:cond-mat/9906360},
year = {2007}
}