Anomalous Fisher-like zeros for the canonical partition function of noninteracting fermions
Department of Physics and Astronomy, McMaster University - Hamilton, Canada L8S 4M1
2 Physics Department, Redeemer University College - Ancaster, Ontario, Canada L9K 1J4
Accepted: 12 October 2011
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.
PACS: 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.) / 05.30.-d – Quantum statistical mechanics
© EPLA, 2011