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On the relation between finite range potentials and subshifts of finite type
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  • Published: December 1995

On the relation between finite range potentials and subshifts of finite type

  • Olle Häggström1 

Probability Theory and Related Fields volume 101, pages 469–478 (1995)Cite this article

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  • 5 Citations

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Summary

Consider a Gibbs potential on the integer lattice ind dimensions for a system with a finite state space. Suppose the interactions are translation invariant and have bounded range (the Ising and Potts models fit into this description). If the parameters of the potential are rational, we show how to construct an equivalent subshift of finite type, in the sense that there is a canonical bijection between Gibbs states for the potential and measures of maximal entropy for the subshift of finite type.

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References

  1. Burton, R., Steif, J.: Nonuniqueness of Measures of Maximal Entropy for Subshifts of Finite Type. Ergodic Theory Dyn. Syst.14, 213–236 (1994)

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  2. Georgii, H.: Gibbs Measures and Phase Transitions. New York: de Gruyter 1988

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  3. Häggström, O.: A Subshift of Finite Type that is Equivalent to the Ising Model. Ergodic Theory Dyn. Syst. (to appear)

  4. Schmidt, K.: Algebraic ideas in ergodic theory. American Mathematical Society. Rhode Island: Providence 1990

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Authors and Affiliations

  1. Mathematics Department, Chalmers University of Technology, S-41296, Göteborg, Sweden

    Olle Häggström

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  1. Olle Häggström
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Häggström, O. On the relation between finite range potentials and subshifts of finite type. Probab. Th. Rel. Fields 101, 469–478 (1995). https://doi.org/10.1007/BF01202780

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  • Received: 23 December 1993

  • Revised: 02 September 1994

  • Issue Date: December 1995

  • DOI: https://doi.org/10.1007/BF01202780

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Mathematics Subject Classification (1991)

  • 60K35
  • 28D15
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