  For the estimation of transition points of finite elastic, flexible polymers
with chain lengths from $13$ to $309$ monomers, we compare systematically
transition temperatures obtained by the Fisher partition function zeros
approach with recent results from microcanonical inflection-point analysis.
These methods rely on accurate numerical estimates of the density of states,
which have been obtained by advanced multicanonical Monte Carlo sampling
techniques. Both the Fisher zeros method and microcanonical inflection-point
analysis yield very similar results and enable the unique identification of
transition points in finite systems, which is typically impossible in the
conventional canonical analysis of thermodynamic quantities.
