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The Ising transducer. (English) Zbl 0724.68062

Summary: The object of this article is to study the transducer which describes the fundamental state of the Ising chain with nonconstant interaction between neighbouring sites.

MSC:

68Q45 Formal languages and automata
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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References:

[1] J.-P. Allouche and M. Mendes France , Quasicrystal Ising Chain and Automata Theory , J. Stat. Phys. , Vol. 42 , 1986 , pp. 809 - 821 . MR 833222 | Zbl 0641.10043 · Zbl 0641.10043 · doi:10.1007/BF01010446
[2] J. Berstel , Transductions and Context-Free Languages , Teubner Studienbücher , 1979 . MR 549481 | Zbl 0424.68040 · Zbl 0424.68040
[3] B. Derrida and E. Gardner , Metastable States of a Spin glass Chain at 0 Temperature , J. Phys. France , Vol. 47 , 1986 , pp. 959 .
[4] B. Derrida , J. Vannimenus and Y. Pomeau , Simple frustrated Systems: Chains, Strips and Squares , J. Phys. C. Solid State Phys. II , 1978 , pp. 4749 - 4765 .
[5] J.M. Luck , Frustration Effects in quasicrystals: an Exactly Soluble Example in One Dimension , J. Phys. A. Lett. , Vol. 20 , 1987 , pp. 1259 - 1268 .
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