Planar quasiperiodic Ising models

Abstract

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.

4 pages, 3 PostScript figures (2 of which have been converted into files with a fixed resolution to meet the limits enforced on file size)

References in corpus (5)

• Aperiodic Ising Quantum Chains
• High-temperature expansion for Ising models on quasiperiodic tilings
• Surface Properties of Aperiodic Ising Quantum Chains
• Coordination Sequences and Critical Points
• Invaded cluster algorithm for critical properties of periodic and aperiodic planar Ising models

Cited by in corpus (7)

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• Q-Dependent Susceptibility in Z-Invariant Pentagrid Ising Model
• Finite-lattice expansion for Ising models on quasiperiodic tilings
• Aperiodicity and Disorder - Does it Matter?
• Partition Function Zeros of Paths and Normalization Zeros of ASEPS
• Partition function zeros of aperiodic Ising models
• Yang-Lee zeros for real-space condensation