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A mathematical proof that the transition to a superconducting state is a second-order phase transition. (English) Zbl 1178.82093
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.

82D55Superconductors (statistical mechanics)
45G10Nonsingular nonlinear integral equations
82C26Dynamic and nonequilibrium phase transitions (general)
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