{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:56:35Z","timestamp":1760241395195,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,1,29]],"date-time":"2018-01-29T00:00:00Z","timestamp":1517184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005357","name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja","doi-asserted-by":"publisher","award":["APVV-16-0186"],"award-info":[{"award-number":["APVV-16-0186"]}],"id":[{"id":"10.13039\/501100005357","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006109","name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","doi-asserted-by":"publisher","award":["VEGA 1\/0331\/15"],"award-info":[{"award-number":["VEGA 1\/0331\/15"]}],"id":[{"id":"10.13039\/501100006109","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The mixed spin-1\/2 and spin-S Ising model on the Union Jack (centered square) lattice with four different three-spin (triplet) interactions and the uniaxial single-ion anisotropy is exactly solved by establishing a rigorous mapping equivalence with the corresponding zero-field (symmetric) eight-vertex model on a dual square lattice. A rigorous proof of the aforementioned exact mapping equivalence is provided by two independent approaches exploiting either a graph-theoretical or spin representation of the zero-field eight-vertex model. An influence of the interaction anisotropy as well as the uniaxial single-ion anisotropy on phase transitions and critical phenomena is examined in particular. It is shown that the considered model exhibits a strong-universal critical behaviour with constant critical exponents when considering the isotropic model with four equal triplet interactions or the anisotropic model with one triplet interaction differing from the other three. The anisotropic models with two different triplet interactions, which are pairwise equal to each other, contrarily exhibit a weak-universal critical behaviour with critical exponents continuously varying with a relative strength of the triplet interactions as well as the uniaxial single-ion anisotropy. It is evidenced that the variations of critical exponents of the mixed-spin Ising models with the integer-valued spins S differ basically from their counterparts with the half-odd-integer spins S.<\/jats:p>","DOI":"10.3390\/e20020091","type":"journal-article","created":{"date-parts":[[2018,1,29]],"date-time":"2018-01-29T12:27:56Z","timestamp":1517228876000},"page":"91","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Strong- and Weak-Universal Critical Behaviour of a Mixed-Spin Ising Model with Triplet Interactions on the Union Jack (Centered Square) Lattice"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1667-6841","authenticated-orcid":false,"given":"Jozef","family":"Stre\u010dka","sequence":"first","affiliation":[{"name":"Department of Theoretical Physics and Astrophysics, Institute of Physics, Faculty of Science, P. J. \u0160af\u00e1rik University, Park Angelinum 9, 040 01 Ko\u0161ice, Slovak Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,29]]},"reference":[{"key":"ref_1","unstructured":"Baxter, R.J. (1982). Exactly Solved Models in Statistical Mechanics, Academic."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/0375-9601(72)90261-7","article-title":"Exact solution of a two dimensional Ising model with pure 3 spin interactions","volume":"41","author":"Hintermann","year":"1972","journal-title":"Phys. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1294","DOI":"10.1103\/PhysRevLett.31.1294","article-title":"Exact Solution of an Ising Model with Three-Spin Interactions on a Triangular Lattice","volume":"31","author":"Baxter","year":"1973","journal-title":"Phys. Rev. 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B"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/2\/91\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:52:59Z","timestamp":1760194379000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/2\/91"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,29]]},"references-count":17,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,2]]}},"alternative-id":["e20020091"],"URL":"https:\/\/doi.org\/10.3390\/e20020091","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,1,29]]}}}