High-temperature expansion for Ising models on quasiperiodic tilings
arXiv:cond-mat/9901001 · doi:10.1088/0305-4470/32/24/306
Abstract
We consider high-temperature expansions for the free energy of zero-field Ising models on planar quasiperiodic graphs. For the Penrose and the octagonal Ammann-Beenker tiling, we compute the expansion coefficients up to 18th order. As a by-product, we obtain exact vertex-averaged numbers of self-avoiding polygons on these quasiperiodic graphs. In addition, we analyze periodic approximants by computing the partition function via the Kac-Ward determinant. For the critical properties, we find complete agreement with the commonly accepted conjecture that the models under consideration belong to the same universality class as those on periodic two-dimensional lattices.
arXiv comment24 pages, 8 figures (EPS), uses IOP styles (included)
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Cited by in corpus (7)
- Planar quasiperiodic Ising models
- Q-Dependent Susceptibility in Z-Invariant Pentagrid Ising Model
- Self-avoiding walks and polygons on quasiperiodic tilings
- Invaded cluster algorithm for critical properties of periodic and aperiodic planar Ising models
- Finite-lattice expansion for Ising models on quasiperiodic tilings
- Fragile magnetic order in metallic quasicrystals
- Stripe order in quasicrystals