Anomalous Fisher-like zeros for the canonical partition function of noninteracting fermions

Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the N-fermion canonical partition function on the positive real β axis (or very close to it), even for a small number of particles. This results in a singular free energy, and instability in other thermal properties of the system. In the context of trapped fermions in a harmonic oscillator, these zeros are shown to be unphysical. Our results are also applicable to mean-field canonical calculations for fermions. By contrast, similar bosonic calculations with continuous density of states yield sensible results.