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In the preceding paper, introducing a cutoff, the present author gave a proofof the statement that the transition to a superconducting state is asecond-order phase transition in the BCS-Bogoliubov model of superconductivityon the basis of fixed-point theorems, and solved the long-standing problem ofthe second-order phase transition from the viewpoint of operator theory. Inthis paper we study the temperature dependence of the specific heat and thecritical magnetic field in the model from the viewpoint of operator theory. Wefirst show some properties of the solution to the BCS-Bogoliubov gap equationwith respect to the temperature, and give the exact and explicit expression forthe gap in the specific heat divided by the specific heat. We then show that itdoes not depend on superconductors and is a universal constant. Moreover, weshow that the critical magnetic field is smooth with respect to thetemperature, and point out the behavior of both the critical magnetic field andits derivative.

An operator-theoretical study of the specific heat and the critical magnetic field in the BCS-Bogoliubov model of superconductivity