Even-odd effect on the thermal equilibrium state of the pairing model. 1. Comparison between canonical and grand canonical ensembles

To facilitate the study of thermal properties of the pairing model, an approach based on the grand canonical ensemble is numerically compared with one based on the canonical ensemble. At low temperature in the phase of pair condensation, their difference becomes significant, in particular with regard to the behavior depending on whether the total number of fermions is even or odd. We separate the grand canonical ensemble into two pieces: one containing systems with even numbers of particles and one containing systems with odd numbers of particles. The grand partition functions defined on such grand canonical ensembles faithfully reproduce the even-odd effect. (author)