Watanabe, Shuji A mathematical proof that the transition to a superconducting state is a second-order phase transition. (English) Zbl 1178.82093 Far East J. Math. Sci. (FJMS) 34, No. 1, 37-57 (2009). There are studied both the gap function and the thermodynamical potential in the BCS-Bogolyubov theory of superconductors. The gap equation is simplified and it does depend only on the temperature. It is pointed out in the paper that the transition from a normal state to a superconducting state is a second-phase transition. The author also establishes that there is a unique \(C^2\) solution on the interval \([0,T_c]\) to the gap equation and there are established further properties of the gap function. Reviewer: Vicenţiu D. Rădulescu (Craiova) Cited in 3 Documents MSC: 82D55 Statistical mechanics of superconductors 45G10 Other nonlinear integral equations 82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics Keywords:second-order phase transition; superconductivity; gap function; thermodynamical potential PDFBibTeX XMLCite \textit{S. Watanabe}, Far East J. Math. Sci. (FJMS) 34, No. 1, 37--57 (2009; Zbl 1178.82093) Full Text: arXiv Link