High-temperature expansion for Ising models on quasiperiodic tilings

We consider high-temperature expansions for the free energy of zero-field I sing models on planar quasiperiodic graphs. For the Penrose and the octagon al Ammann-Beenker tiling, we compute the expansion coefficients up to 18th order. As a by-product, we obtain exact vertex-averaged numbers of self-avo iding polygons on these quasiperiodic graphs. In addition, we analyse perio dic approximants by computing the partition function via the Kac-Ward deter minant. It turns out that the series expansions alone do not yield reliable estimates of the critical exponents. This is due to the limitation on the order of the series caused by the number of graphs that have to be taken in to account, and, more seriously, to rather strong fluctuations in the behav iour of the coefficients. Nevertheless, our results are compatible with the commonly accepted conjecture that the models under consideration belong to the same universality class as those on periodic two-dimensional lattices.