Thermal dependence of pairing correlations in small superconducting particles in a finite magnetic field

We investigate the thermal behavior of pairing correlations in nanoscale particles in the presence of a magnetic field. By computing the exact partition function in a small system, it is shown that at finite fields, these correlations may behave in a nonmonotonous way with increasing temperature in both the even and odd systems, leading to characteristic signatures of pairing effects in the magnetization, which are seen to subsist up to extremely small sizes. Results obtained with the static path plus random phase approximation in larger configuration spaces exhibit the same features. The peculiar thermal behavior of the BCS gap for finite fields and odd parity is also examined.