{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:48:04Z","timestamp":1760244484884,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,3]],"date-time":"2022-12-03T00:00:00Z","timestamp":1670025600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CONACyT-Mexico","award":["CF-2019-1327701"],"award-info":[{"award-number":["CF-2019-1327701"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2014a correspondence which was later formalized by O. H\u00e4ggstr\u00f6m. 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.<\/jats:p>","DOI":"10.3390\/e24121772","type":"journal-article","created":{"date-parts":[[2022,12,5]],"date-time":"2022-12-05T02:56:26Z","timestamp":1670208986000},"page":"1772","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Correspondence between Subshifts of Finite Type and Statistical Mechanics Models"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3407-5660","authenticated-orcid":false,"given":"Luis Armando","family":"Corona","sequence":"first","affiliation":[{"name":"Instituto de Investigaci\u00f3n en Ciencias B\u00e1sicas y Aplicadas, Universidad Aut\u00f3noma del Estado de Morelos, Cuernavaca 62209, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3150-065X","authenticated-orcid":false,"given":"Ra\u00fal","family":"Salgado Garc\u00eda","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Ciencias-IICBA, Universidad Aut\u00f3noma del Estado de Morelos, Cuernavaca 62209, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edgardo","family":"Ugalde","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidad Aut\u00f3noma de San Luis Potos\u00ed, San Luis Potosi 78250, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kitchens, B.P. (1998). Symbolic Dynamics: One-Sided, Two-Sided and Countable State Markov Shifts, Springer.","DOI":"10.1007\/978-3-642-58822-8_7"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1017\/S0143385700007859","article-title":"Non-uniqueness of measures of maximal entropy for subshifts of finite type","volume":"14","author":"Burton","year":"1994","journal-title":"Ergod. Theory Dyn. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/BF02808205","article-title":"New results on measures of maximal entropy","volume":"89","author":"Burton","year":"1995","journal-title":"Isr. J. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1017\/S0143385700008518","article-title":"A subshift of finite type that is equivalent to the Ising model","volume":"15","year":"1995","journal-title":"Ergod. Theory Dyn. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/BF01202780","article-title":"On the relation between finite range potentials and subshifts of finite type","volume":"101","year":"1995","journal-title":"Probab. Theory Relat. Fields"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1007\/BF01212295","article-title":"An Alternate Version of Pirogov-Sinai Theory","volume":"93","year":"1984","journal-title":"Commun. Math. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Georgii, H. (2011). Gibbs Measures and Phase Transitions, de Gruyter.","DOI":"10.1515\/9783110250329"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1017\/S0305004100027419","article-title":"Some Generalized Order-Disorder Transformations","volume":"48","author":"Potts","year":"1952","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1103\/PhysRev.60.252","article-title":"Statistics of the Two-Dimensional Ferromagnet. Part I","volume":"60","author":"Kramers","year":"1941","journal-title":"Phys. Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1103\/PhysRev.60.263","article-title":"Statistics of the Two-Dimensional Ferromagnet. Part II","volume":"60","author":"Kramers","year":"1941","journal-title":"Phys. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/BF01211103","article-title":"Translation Invariant Gibbs States in the q-State Potts Model","volume":"105","author":"Martirosian","year":"1986","journal-title":"Commun. Math. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"L445","DOI":"10.1088\/0022-3719\/6\/23\/005","article-title":"Potts model at the critical temperature","volume":"6","author":"Baxter","year":"1973","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_13","first-page":"1363","article-title":"Discontinuity of the phase transition for the planar random-cluster and Potts models with q > 4","volume":"54","author":"Gagnebin","year":"2021","journal-title":"Ann. Sci. l\u2019ENS"},{"key":"ref_14","first-page":"75","article-title":"Sharp phase transition for the random-cluster and Potts models via decision trees","volume":"189","author":"Raoufi","year":"2019","journal-title":"Ann. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1103\/PhysRev.65.117","article-title":"Crystal statistics. 1. A Two-dimensional model with an order disorder transition","volume":"65","author":"Onsager","year":"1944","journal-title":"Phys. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1063\/1.1665583","article-title":"Zeros of the Partition Function for the Heisenberg, Ferroelectric, and General Ising Models","volume":"12","author":"Suzuki","year":"1971","journal-title":"J. Math. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1007\/BF01011773","article-title":"Exact Results for the Potts Model in Two Dimensions","volume":"19","author":"Hintermann","year":"1978","journal-title":"J. Stat. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1007\/s00440-011-0353-8","article-title":"The self-dual point of the two-dimensional random-cluster model is critical for q \u2265 1","volume":"153","author":"Beffara","year":"2012","journal-title":"Probab. Theory Relat. Fields"},{"key":"ref_19","unstructured":"Baxter, R.J. (1982). Exactly Solved Models in Statistical Mechanics, Academic Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1007\/s00220-022-04459-x","article-title":"On the Six-Vertex Model\u2019s Free Energy","volume":"395","author":"Kozlowski","year":"2022","journal-title":"Commun. Math. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1103\/PhysRev.162.162","article-title":"Residual entropy of squared Ice","volume":"162","author":"Lieb","year":"1967","journal-title":"Phys. Rev."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"7053","DOI":"10.1088\/0305-4470\/33\/40\/304","article-title":"Thermodynamic limit of the six-vertex model with domain wall boundary conditions","volume":"33","author":"Korepin","year":"2000","journal-title":"J. Phys. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s00440-013-0486-z","article-title":"On the Gibbs states of the noncritical Potts model on \n\t\t  Z2","volume":"158","author":"Coquille","year":"2013","journal-title":"Probab. Theory Relat. Fields"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/978-3-030-32011-9_2","article-title":"Lectures on the Ising and Potts Models on the Hypercubic Lattice","volume":"Volume 304","author":"Barlow","year":"2020","journal-title":"Random Graphs, Phase Transitions, and the Gaussian Free Field"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1772\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:33:41Z","timestamp":1760146421000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1772"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,3]]},"references-count":24,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["e24121772"],"URL":"https:\/\/doi.org\/10.3390\/e24121772","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,12,3]]}}}