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Quasicrystal Ising chain and automata theory. (English) Zbl 0641.10043

Summary: An automatic sequence is generated by a finite machine (automaton). These sequences can be periodic or not: in the latter case however, they are not random, but rather “quasicrystalline”. We consider an Ising chain with variable interaction in a uniform external field, at zero temperature, and prove that, if this interaction is automatic, then the induced magnetic field is also automatic.

MSC:

11B99 Sequences and sets
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
37B99 Topological dynamics
68Q45 Formal languages and automata
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