The solution to the BCS gap equation and the second-order phase transition in superconductivity (Q2275498)

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.