  We investigate zero-field Ising models on periodic approximants of planar
quasiperiodic tilings by means of partition function zeros and high-temperature
expansions. These are obtained by employing a determinant expression for the
partition function. The partition function zeros in the complex temperature
plane yield precise estimates of the critical temperature of the quasiperiodic
model. Concerning the critical behaviour, our results are compatible with
Onsager universality, in agreement with the Harris-Luck criterion based on
scaling arguments.
