  For real inverse temperature beta, the canonical partition function is always
positive, being a sum of positive terms. There are zeros, however, on the
complex beta plane that are called Fisher zeros. In the thermodynamic limit,
the Fisher zeros coalesce into continuous curves. In case there is a phase
transition, the zeros tend to pinch the real-beta axis. For an ideal trapped
Bose gas in an isotropic three-dimensional harmonic oscillator, this tendency
is clearly seen, signalling Bose-Einstein condensation (BEC). The calculation
can be formulated exactly in terms of the virial expansion with
temperature-dependent virial coefficients. When the second virial coefficient
of a strongly interacting attractive unitary gas is included in the
calculation, BEC seems to survive, with the condensation temperature shifted to
a lower value for the unitary gas. This shift is consistent with a direct
calculation of the heat capacity from the canonical partition function of the
ideal and the unitary gas.
