Abstract
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.
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Allouche, JP., France, M.M. Quasicrystal Ising chain and automata theory. J Stat Phys 42, 809–821 (1986). https://doi.org/10.1007/BF01010446
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DOI: https://doi.org/10.1007/BF01010446