Critical point of the transition between $s_{\pm }$ and $s_{++}$ states of a two-band superconductor with nonmagnetic impurities

Behavior of the Grand thermodynamic potential along with its derivatives, entropy and specific heat, is considered within a two-band model of an unconventional $s_{\pm }$ superconductor with nonmagnetic impurities. The transition $s_{\pm }\to s_{++}$ is shown to be a smooth crossover at high temperatures, while it becomes the first order phase transition at low temperatures. Thus, on a phase diagram temperature'-impurity scattering rate’ there appears to be a critical end point. Temperature at which the behavior of the transition is changed is maximal in the Born limit and tends to zero away from the limit, which points out to the possible realization of a quantum phase transition.