{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:43:29Z","timestamp":1760118209107,"version":"build-2065373602"},"reference-count":57,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T00:00:00Z","timestamp":1735257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ANID Fondecyt (Chile)","award":["1230055","1240582","NNBP NCN2021 _021","UTFSM DGIIE","11221088","DGII-UTA"],"award-info":[{"award-number":["1230055","1240582","NNBP NCN2021 _021","UTFSM DGIIE","11221088","DGII-UTA"]}]},{"name":"UTFSM DPP","award":["1230055","1240582","NNBP NCN2021 _021","UTFSM DGIIE","11221088","DGII-UTA"],"award-info":[{"award-number":["1230055","1240582","NNBP NCN2021 _021","UTFSM DGIIE","11221088","DGII-UTA"]}]},{"name":"Millennium Nucleus in NanoBioPhysics","award":["1230055","1240582","NNBP NCN2021 _021","UTFSM DGIIE","11221088","DGII-UTA"],"award-info":[{"award-number":["1230055","1240582","NNBP NCN2021 _021","UTFSM DGIIE","11221088","DGII-UTA"]}]},{"name":"ANID Iniciaci\u00f3n en Investigaci\u00f3n Fondecyt Grant","award":["1230055","1240582","NNBP NCN2021 _021","UTFSM DGIIE","11221088","DGII-UTA"],"award-info":[{"award-number":["1230055","1240582","NNBP NCN2021 _021","UTFSM DGIIE","11221088","DGII-UTA"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work, we study the magnetocaloric effect (MCE) in a working substance corresponding to a square lattice of spins with Q possible orientations, known as the \u201cQ-state clock model\u201d. When the Q-state clock model has Q\u22655 possible configurations, it presents the famous Berezinskii\u2013Kosterlitz\u2013Thouless (BKT) phase associated with vortex states. We calculate the thermodynamic quantities using Monte Carlo simulations for even Q numbers, ranging from Q=2 to Q=8 spin orientations per site in a lattice. We use lattices of different sizes with N=L\u00d7L=82,162,322,642,and1282 sites, considering free boundary conditions and an external magnetic field varying between B=0 and B=1.0 in natural units of the system. By obtaining the entropy, it is possible to quantify the MCE through an isothermal process in which the external magnetic field on the spin system is varied. In particular, we find the values of Q that maximize the MCE depending on the lattice size and the magnetic phase transitions linked with the process. Given the broader relevance of the Q-state clock model in areas such as percolation theory, neural networks, and biological systems, where multi-state interactions are essential, our study provides a robust framework in applied quantum mechanics, statistical physics, and related fields.<\/jats:p>","DOI":"10.3390\/e27010011","type":"journal-article","created":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T02:59:27Z","timestamp":1735268367000},"page":"11","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Magnetocaloric Effect for a Q-Clock-Type System"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3049-668X","authenticated-orcid":false,"given":"Michel","family":"Aguilera","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, Casilla 4950, Valpara\u00edso 2373223, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6884-6067","authenticated-orcid":false,"given":"Sergio","family":"Pino-Alarc\u00f3n","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Av. Espa\u00f1a 1680, Valpara\u00edso 2390123, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7432-0707","authenticated-orcid":false,"given":"Francisco J.","family":"Pe\u00f1a","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Av. Espa\u00f1a 1680, Valpara\u00edso 2390123, Chile"},{"name":"Millennium Nucleus in NanoBioPhysics (NNBP), Av. Espa\u00f1a 1680, Valpara\u00edso 2390123, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1701-3030","authenticated-orcid":false,"given":"Eugenio E.","family":"Vogel","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias F\u00edsicas, Universidad de La Frontera, Casilla 54-D, Temuco 4811230, Chile"},{"name":"Facultad de Ingenier\u00eda, Universidad Central de Chile, Santiago 8330601, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9261-2394","authenticated-orcid":false,"given":"Natalia","family":"Cort\u00e9s","sequence":"additional","affiliation":[{"name":"Instituto de Alta Investigaci\u00f3n, Universidad de Tarapac\u00e1, Casilla 7D, Arica 1000000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9235-9747","authenticated-orcid":false,"given":"Patricio","family":"Vargas","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Av. Espa\u00f1a 1680, Valpara\u00edso 2390123, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100028","DOI":"10.1016\/j.physo.2020.100028","article-title":"Caloric effects of quantum materials: An outlook","volume":"4","author":"Reis","year":"2020","journal-title":"Phys. Open"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1971","DOI":"10.1007\/s10948-018-4666-z","article-title":"Review on magnetocaloric effect and materials","volume":"31","author":"Ram","year":"2018","journal-title":"J. Supercond. Nov. Magn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"101380","DOI":"10.1016\/j.tsep.2022.101380","article-title":"Cooling through barocaloric effect: A review of the state of the art up to 2022","volume":"33","author":"Cirillo","year":"2022","journal-title":"Therm. Sci. Eng. 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