{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,2]],"date-time":"2026-11-02T23:06:34Z","timestamp":1793660794356,"version":"4.5.1"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,7]],"date-time":"2021-08-07T00:00:00Z","timestamp":1628294400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model presents an intermediate vortex state when the number of possible orientations q for the system is greater than or equal to 5. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit q\u2192\u221e. Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters.<\/jats:p>","DOI":"10.3390\/e23081019","type":"journal-article","created":{"date-parts":[[2021,8,8]],"date-time":"2021-08-08T21:49:41Z","timestamp":1628459381000},"page":"1019","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Short-Range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-State Clock Model"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2412-8602","authenticated-orcid":false,"given":"Oscar A.","family":"Negrete","sequence":"first","affiliation":[{"name":"Department of Physics, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Vapara\u00edso 2390123, Chile"},{"name":"Center for the Development of Nanoscience and Nanotechnology, Santiago 8320000, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9235-9747","authenticated-orcid":false,"given":"Patricio","family":"Vargas","sequence":"additional","affiliation":[{"name":"Department of Physics, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Vapara\u00edso 2390123, Chile"},{"name":"Center for the Development of Nanoscience and Nanotechnology, Santiago 8320000, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7432-0707","authenticated-orcid":false,"given":"Francisco J.","family":"Pe\u00f1a","sequence":"additional","affiliation":[{"name":"Department of Physics, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Vapara\u00edso 2390123, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gonzalo","family":"Saravia","sequence":"additional","affiliation":[{"name":"Department of Physics, Universidad de La Frontera, Casilla 54-D, Temuco 4811230, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eugenio E.","family":"Vogel","sequence":"additional","affiliation":[{"name":"Center for the Development of Nanoscience and Nanotechnology, Santiago 8320000, Chile"},{"name":"Department of Physics, Universidad de La Frontera, Casilla 54-D, Temuco 4811230, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"L181","DOI":"10.1088\/0022-3719\/19\/8\/005","article-title":"The infinite-range clock spin glass model: An investigation of the relevance of reflection symmetry","volume":"19","author":"Nobre","year":"1986","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"032124","DOI":"10.1103\/PhysRevE.87.032124","article-title":"High q-state clock spin glasses in three dimensions and the Lyapunov exponents of chaotic phases and chaotic phase boundaries","volume":"87","author":"Ilker","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"062112","DOI":"10.1103\/PhysRevE.90.062112","article-title":"Odd q-state clock spin-glass models in three dimensions, asymmetric phase diagrams, and multiple algebraically ordered phases","volume":"90","author":"Ilker","year":"2014","journal-title":"Phys. Rev. E"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1103\/PhysRevB.16.1217","article-title":"Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model","volume":"16","author":"Jose","year":"1977","journal-title":"Phys. Rev. B"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"041120","DOI":"10.1103\/PhysRevE.83.041120","article-title":"Numerical study of the phase transitions in the two-dimensional Z(5) vector model","volume":"83","author":"Borisenko","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_6","unstructured":"Landau, L.D., Lifshitz, E.M., and Pitaevskii, E.M. (1999). Statistical Physics, Butterworth-Heinemann."},{"key":"ref_7","first-page":"907","article-title":"Destruction of Long-range Order in One-dimensional and Two-dimensional Systems having a Continuous Symmetry Group I. Classical Systems","volume":"59","author":"Berezinskii","year":"1971","journal-title":"Zh. Eksp. Teor. Fiz."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"L124","DOI":"10.1088\/0022-3719\/5\/11\/002","article-title":"Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory)","volume":"5","author":"Kosterlitz","year":"1972","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1088\/0022-3719\/6\/7\/010","article-title":"Ordering, metastability and phase transitions in two-dimensional systems","volume":"6","author":"Kosterlitz","year":"1973","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1046","DOI":"10.1088\/0022-3719\/7\/6\/005","article-title":"The critical properties of the two-dimensional xy model","volume":"7","author":"Kosterlitz","year":"1974","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6899","DOI":"10.1103\/PhysRevB.25.6899","article-title":"Random symmetry-breaking fields and the XY model","volume":"25","author":"Cardy","year":"1982","journal-title":"Phys. Rev. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1103\/PhysRevLett.74.606","article-title":"Replica Symmetry Breaking Instability in the 2D XY Model in a Random Field","volume":"74","author":"Doussal","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"054433","DOI":"10.1103\/PhysRevB.95.054433","article-title":"Approximating the XY model on a random graph with a q-state clock model","volume":"95","author":"Lupo","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Negrete, O.A., Vargas, P., Pe\u00f1a, F.J., Saravia, G., and Vogel, E.E. (2018). Entropy and Mutability for the q-state Clock Model in Small Systems. Entropy, 20.","DOI":"10.20944\/preprints201811.0296.v1"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3698","DOI":"10.1103\/PhysRevD.19.3698","article-title":"Phase structure of discrete Abelian spin and gauge systems","volume":"19","author":"Elitzur","year":"1979","journal-title":"Phys. Rev. D"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1088\/0305-4470\/13\/4\/037","article-title":"General discrete planar models in two dimensions: Duality properties and phase diagrams","volume":"13","author":"Cardy","year":"1980","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/BF01208273","article-title":"The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas","volume":"81","author":"Spencer","year":"1981","journal-title":"Commun. Math. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1016\/j.nuclphysb.2011.09.012","article-title":"Dualities and the phase diagram of the p-clock model","volume":"854","author":"Ortiz","year":"2012","journal-title":"Nucl. Phys. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"104427","DOI":"10.1103\/PhysRevB.88.104427","article-title":"Response to a twist in systems with Zp symmetry: The two-dimensional p-state clock model","volume":"88","author":"Kumano","year":"2013","journal-title":"Phys. Rev. B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"052130","DOI":"10.1103\/PhysRevE.96.052130","article-title":"Partition function zeros of the p-state clock model in the complex temperature plan","volume":"96","author":"Kim","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"060105","DOI":"10.1103\/PhysRevE.101.060105","article-title":"Critical properties of the two-dimensional q-state clock model","volume":"101","author":"Li","year":"2020","journal-title":"Phys. Rev. E"},{"key":"ref_22","unstructured":"Kenna, R. (2005). The XY Model and the Berezinskii-Kosterlitz-Thouless Phase Transition. arXiv."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Jose, J.V. (2013). 40 Years of Berezinskii-Kosterlitz-Thouless Theory, World Scientific.","DOI":"10.1142\/8572"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"032109","DOI":"10.1103\/PhysRevE.98.032109","article-title":"Ordering kinetics in the q-state clock model: Scaling properties and growth laws","volume":"98","author":"Chatterjee","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BF01293604","article-title":"Finite size scaling analysis of ising model block distribution functions","volume":"119","author":"Binder","year":"1981","journal-title":"Z. Phys. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1088\/0034-4885\/60\/5\/001","article-title":"Applications of Monte Carlo methods to statistical physics","volume":"60","author":"Binder","year":"1997","journal-title":"Rep. Prog. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"060101R","DOI":"10.1103\/PhysRevE.80.060101","article-title":"True and quasi-long-range order in the generalized q-state clock model","volume":"80","author":"Baek","year":"2009","journal-title":"Phys. Rev. E"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4075","DOI":"10.1016\/j.physa.2009.06.010","article-title":"Phase transitions in Edwards-Anderson model by means of information theory","volume":"388","author":"Vogel","year":"2009","journal-title":"Physica A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1016\/j.physa.2011.09.005","article-title":"Data compressor designed to improve recognition of magnetic phases","volume":"391","author":"Vogel","year":"2012","journal-title":"Physica A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.jmmm.2014.07.055","article-title":"Phase diagram and reentrance for the 3D Edwards-Anderson model using information theory","volume":"372","author":"Cortez","year":"2014","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1140\/epjb\/e2014-41003-0","article-title":"Information theory applied to econophysics: Stock market behaviors","volume":"87","author":"Vogel","year":"2014","journal-title":"Eur. Phys. J. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1016\/j.physa.2015.01.023","article-title":"Information theory as a tool to improve individual pensions: The Chilean case","volume":"424","author":"Vogel","year":"2015","journal-title":"Physica A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.jash.2015.12.010","article-title":"Derivation of a measure of systolic blood pressure mutability: A novel information theory-based metric from ambulatory blood pressure tests","volume":"10","author":"Contreras","year":"2016","journal-title":"J. Am. Soc. Hypertens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1016\/j.tecto.2017.06.031","article-title":"Time-series analysis of earthquake sequences by means of information recognizer","volume":"712","author":"Vogel","year":"2017","journal-title":"Tectonophysics"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"062133","DOI":"10.1103\/PhysRevE.96.062133","article-title":"Phase diagrams in a system of long rods on two-dimensional lattices by means of information theory","volume":"96","author":"Vogel","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1016\/j.renene.2018.03.064","article-title":"A novel method to optimize electricity generation from wind energy","volume":"126","author":"Vogel","year":"2018","journal-title":"Renew. Energy"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"022104","DOI":"10.1103\/PhysRevE.101.022104","article-title":"Alternative characterization of the nematik transition in deposition of rods on two-dimensional lattices","volume":"101","author":"Vogel","year":"2020","journal-title":"Phys. Rev. E"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/1019\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:42:13Z","timestamp":1760164933000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/1019"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,7]]},"references-count":37,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["e23081019"],"URL":"https:\/\/doi.org\/10.3390\/e23081019","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints202107.0291.v1","asserted-by":"object"}]},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,7]]}}}