{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T08:52:12Z","timestamp":1768294332422,"version":"3.49.0"},"reference-count":46,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,29]],"date-time":"2024-01-29T00:00:00Z","timestamp":1706486400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Italian Ministry of Research PRIN","award":["2020F3NCPX_001"],"award-info":[{"award-number":["2020F3NCPX_001"]}]},{"name":"Italian Ministry of Research PRIN","award":["pMI22_FisCo"],"award-info":[{"award-number":["pMI22_FisCo"]}]},{"name":"CINECA project High Performance Computing","award":["2020F3NCPX_001"],"award-info":[{"award-number":["2020F3NCPX_001"]}]},{"name":"CINECA project High Performance Computing","award":["pMI22_FisCo"],"award-info":[{"award-number":["pMI22_FisCo"]}]},{"name":"Mathematics for Industry 4.0 (Math4I4)","award":["2020F3NCPX_001"],"award-info":[{"award-number":["2020F3NCPX_001"]}]},{"name":"Mathematics for Industry 4.0 (Math4I4)","award":["pMI22_FisCo"],"award-info":[{"award-number":["pMI22_FisCo"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in the full-anisotropy limit. We show that a comprehensive understanding of the dynamic behavior of systems with quenched defects requires a generalized definition of the dynamic order parameter. By doing so, we demonstrate that the inclusion of quenched defects lowers the dynamic critical temperature as well, with a linear trend across the range of defect fractions considered. We also explore if and how it is possible to predict the dynamic behavior of specific magnetic systems with quenched randomness. Various geometric quantities, such as a defect potential index, the defect dipole moment, and the properties of the defect Delaunay triangulation, prove useful for this purpose.<\/jats:p>","DOI":"10.3390\/e26020120","type":"journal-article","created":{"date-parts":[[2024,1,29]],"date-time":"2024-01-29T08:54:03Z","timestamp":1706518443000},"page":"120","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects"],"prefix":"10.3390","volume":"26","author":[{"given":"Federico","family":"Ettori","sequence":"first","affiliation":[{"name":"Department of Physics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thibaud","family":"Coup\u00e9","sequence":"additional","affiliation":[{"name":"Department of Physics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9163-0061","authenticated-orcid":false,"given":"Timothy J.","family":"Sluckin","sequence":"additional","affiliation":[{"name":"Department of Physics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy"},{"name":"School of Mathematical Sciences, University of Southampton, University Road, Highfield, Southampton SO17 1BJ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8382-3621","authenticated-orcid":false,"given":"Ezio","family":"Puppin","sequence":"additional","affiliation":[{"name":"Department of Physics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9299-6340","authenticated-orcid":false,"given":"Paolo","family":"Biscari","sequence":"additional","affiliation":[{"name":"Department of Physics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,29]]},"reference":[{"key":"ref_1","unstructured":"Bak, P. 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