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. 2022 Dec 3;24(12):1772.
doi: 10.3390/e24121772.

On the Correspondence between Subshifts of Finite Type and Statistical Mechanics Models

Luis Armando Corona  1 , Raúl Salgado García  2 , Edgardo Ugalde  3
Affiliations

On the Correspondence between Subshifts of Finite Type and Statistical Mechanics Models

Luis Armando Corona et al. Entropy (Basel). .

Abstract

Several classical problems in symbolic dynamics concern the characterization of the simplex of measures of maximal entropy. For subshifts of finite type in higher dimensions, methods of statistical mechanics are ideal for dealing with these problems. R. Burton and J. Steif developed a strategy to construct examples of strongly irreducible subshifts of finite type admitting several measures of maximal entropy. This strategy exploits a correspondence between equilibrium statistical mechanics and symbolic dynamics-a correspondence which was later formalized by O. Häggström. In this paper, we revisit and discuss this correspondence with the aim of presenting a simplified version of it and present some applications of rigorous results concerning the Potts model and the six-vertex model to symbolic dynamics, illustrating in this way the possibilities of this correspondence.

Keywords: phase transitions; statistical mechanics models; subshifts of finite type.

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Conflict of interest statement

The authors declare no conflict of interest.

References

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