Planar quasiperiodic Ising models

We investigate zero-field Ising models on periodic approximants of planar q uasiperiodic tilings by means of partition function zeros and high-temperat ure expansions. These are obtained by employing a determinant expression fo r the partition function. The partition function zeros in the complex tempe rature plane yield precise estimates of the critical temperature of the qua siperiodic model. Concerning the critical behaviour, our results are compat ible with Onsager universality, in agreement with the Harris-Luck criterion based on scaling arguments. (C) 2000 Elsevier Science B.V. All rights rese rved.