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The solution to the BCS gap equation and the second-order phase transition in superconductivity. (English) Zbl 1223.82074
The first part of the present paper is devoted to an alternative proof of the existence of a unique solution to the BCS gap equation. Next, it is defined a certain subspace $W$ of a Banach space consisting of continuous functions and it is considered the solution approximated by an element of $W$. Next, it is shown that, under this approximation, the transition to a superconducting state is a second-order phase transition. In other words, it is established that the condition that the solution belongs to $W$ is a sufficient condition for the second-order phase transition to superconductivity.
##### MSC:
 82D55 Superconductors (statistical mechanics) 82B26 Phase transitions (general) 45G10 Nonsingular nonlinear integral equations