A mathematical proof that the transition to a superconducting state is a second-order phase transition

Abstract

We deal with the gap function and the thermodynamical potential in the BCS-Bogoliubov theory of superconductivity, where the gap function is a function of the temperature $T$ only. We show that the squared gap function is of class $C^2$ on the closed interval $[0,T_c]$ and point out some more properties of the gap function. Here, $T_c$ stands for the transition temperature. On the basis of this study we then give, examining the thermodynamical potential, a mathematical proof that the transition to a superconducting state is a second-order phase transition. Furthermore, we obtain a new and more precise form of the gap in the specific heat at constant volume from a mathematical point of view.

16 pages

References in corpus (1)

• Spectral properties of the BCS gap equation of superfluidity

Cited by in corpus (5)

• Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems
• The solution to the BCS gap equation and the second-order phase transition in superconductivity
• Is the solution to the BCS gap equation continuous in the temperature ?
• An operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity (final version)
• Lipschitz continuity and monotone decreasingness of the solution to the BCS gap equation for superconductivity