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.
References
Burton, R., Steif, J.: Nonuniqueness of Measures of Maximal Entropy for Subshifts of Finite Type. Ergodic Theory Dyn. Syst.14, 213–236 (1994)
Georgii, H.: Gibbs Measures and Phase Transitions. New York: de Gruyter 1988
Häggström, O.: A Subshift of Finite Type that is Equivalent to the Ising Model. Ergodic Theory Dyn. Syst. (to appear)
Schmidt, K.: Algebraic ideas in ergodic theory. American Mathematical Society. Rhode Island: Providence 1990
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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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DOI: https://doi.org/10.1007/BF01202780
Mathematics Subject Classification (1991)
- 60K35
- 28D15