A spin-flip potential V is added to a BCS Hamiltonian in order to study its effect on the superconducting phase from a statistical physics point of view. The spin-flip potential could also be understood as a simplified way of representing the effect of impurities in a conventional superconductor. We found that the competition between the pairing and the spin-flip effect gives rise to a first-order phase transition for a range of values of V, before the total destruction of the superconducting order. The phase diagram shows a tricritical point in a frontier line which is topologically similar to those found in the phase diagrams of some Ising-like models as the Blume–Capel model. The first-order frontier was obtained numerically by free energy minimization.