Partition function zeros of aperiodic Ising models

Grimm, Uwe and Repetowicz, Przemyslaw (2002). Partition function zeros of aperiodic Ising models. In: Kapuscik, Edward and Horzela, Andrzej eds. Quantum Theory and Symmetries. Singapore: World Scientific, pp. 354–359.

URL: http://www.worldscibooks.com/physics/4908.html

Abstract

We consider Ising models defined on periodic approximants of aperiodic graphs. The model contains only a single coupling constant and no magnetic field, so the aperiodicity is entirely given by the different local environments of neighbours in the aperiodic graph. In this case, the partition function zeros in the temperature variable, also known as the Fisher zeros, can be calculated by diagonalisation of finite matrices. We present the partition function zero patterns for periodic approximants of the Penrose and the Ammann-Beenker tiling, and derive precise estimates of the critical temperatures.

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About

• Item ORO ID
• 12352
• Item Type
• Book Section
• ISBN
• 981-02-4887-3, 978-981-02-4887-1
• Extra Information
• Proceedings of the Second International Symposium
  Kraków, Poland 18 - 21 July 2001
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Uwe Grimm