Abstract
We study partition functions and thermodynamic limits for the Ising model on three families of finite graphs converging to infinite self-similar graphs. They are provided by three well-known groups realized as automorphism groups of regular rooted trees: the first Grigorchuk’s group of intermediate growth; the iterated monodromy group of the complex polynomial z 2-1 known as the “Basilica group”; and the Hanoi Towers group H (3) closely related to the Sierpinski gasket.
Mathematics Subject Classification (2000). Primary 82B20; Secondary 05A15.
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D’Angeli, D., Donno, A., Nagnibeda, T. (2011). Partition Functions of the Ising Model on Some Self-similar Schreier Graphs. In: Lenz, D., Sobieczky, F., Woess, W. (eds) Random Walks, Boundaries and Spectra. Progress in Probability, vol 64. Springer, Basel. https://doi.org/10.1007/978-3-0346-0244-0_15
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DOI: https://doi.org/10.1007/978-3-0346-0244-0_15
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