Partition functions of the Ising model on some self-similar Schreier graphs

Details Partition functions of the Ising model on some self-similar Schreier graphs Partition functions of the Ising model on some self-similar Schreier graphs

2010-03-02

arxiv.org/abs/1003.0611v1

Progress in Probability: Random Walks, Boundaries and Spectra (D.Lenz, F. Sobieczky and W. Woess editors), 64 (2011), 277-304,

Mathematics

Combinatorics

23 pages

Scientific paper

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 Sierpinsky gasket.

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