Some universal relations between the gap and thermodynamic functions plausible for various models of superconductors

It is proven that there exist some universal relations between the energy gap and the differences of the thermodynamic potential, entropy, specific heat and critical magnetic field for many two- and three-dimensional models of superconductivity with spin-singlet Cooper pairs forming \textit{s} or \textit{d} or \textit{g} etc. states. The obtained formulae make it possible to derive thermodynamic functions and, in particular, the superconducting specific heat and the critical magnetic induction in the whole temperature range $0\leq T\leq T_{c}$ employing the form of $Δ(T)$ only. The inverse formula allowing us to find $Δ(T)$, when the temperature dependence of the specific heat difference is known, is also presented. The results are referred to some obtained within the McMillan formalism, and some remarks on an application of the present formulae to the {\textit{t--J}} model are given.

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