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Fractal symmetry in an Ising model. (English) Zbl 0714.60104

The authors present a short-range Ising model with translational invariant four-body interaction, for which the ground state is unique and has two striking properties: it has both discrete and continuous spectra and has a fractal symmetry in the sense that its correlation functions are invariant under doubling of the distance.
Reviewer: M.Mürmann

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
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