{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T19:03:32Z","timestamp":1790708612553,"version":"4.1.0"},"reference-count":29,"publisher":"American Physical Society (APS)","issue":"1","license":[{"start":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T00:00:00Z","timestamp":1737417600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-license"}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2025,1,7]]},"DOI":"10.1103\/physreve.111.015305","type":"journal-article","created":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T10:06:41Z","timestamp":1737454001000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Critical temperature of the classical\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mrow>\n                        <mml:mi mathvariant=\"italic\">XY<\/mml:mi>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    model via autoencoder latent space sampling"],"prefix":"10.1103","volume":"111","author":[{"given":"Brandon","family":"Willnecker","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04qzfn040","id-type":"ROR","asserted-by":"publisher"}],"name":"University of KwaZulu-Natal"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2885-904X","authenticated-orcid":true,"given":"Mervlyn","family":"Moodley","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04qzfn040","id-type":"ROR","asserted-by":"publisher"}],"name":"University of KwaZulu-Natal"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,1,21]]},"reference":[{"key":"PhysRevE.111.015305Cc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.91.045002","type":"journal-article"},{"key":"PhysRevE.111.015305Cc2R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-648X\/abb895","type":"journal-article"},{"key":"PhysRevE.111.015305Cc3R1","doi-asserted-by":"publisher","DOI":"10.1038\/nphys4035","type":"journal-article"},{"key":"PhysRevE.111.015305Cc4R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.94.195105","type":"journal-article"},{"key":"PhysRevE.111.015305Cc5R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.118.216401","type":"journal-article"},{"key":"PhysRevE.111.015305Cc6R1","doi-asserted-by":"publisher","DOI":"10.5488\/CMP.21.33602","type":"journal-article"},{"key":"PhysRevE.111.015305Cc7R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-019-0512-x","type":"journal-article"},{"key":"PhysRevE.111.015305Cc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.97.045207","type":"journal-article"},{"key":"PhysRevE.111.015305Cc9R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-019-0554-0","type":"journal-article"},{"key":"PhysRevE.111.015305Cc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.99.032142","type":"journal-article"},{"key":"PhysRevE.111.015305Cc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.108.214428","type":"journal-article"},{"key":"PhysRevE.111.015305Cc12R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-020-58263-5","type":"journal-article"},{"key":"PhysRevE.111.015305Cc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.107.134420","type":"journal-article"},{"key":"PhysRevE.111.015305Cc14R1","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690370209","type":"journal-article"},{"key":"PhysRevE.111.015305Cc17R1","volume-title":"Neural Networks and Deep Learning","author":"M.\u00a0A. Nielsen","year":"2015","type":"book"},{"key":"PhysRevE.111.015305Cc18R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.17.1307","type":"journal-article"},{"key":"PhysRevE.111.015305Cc19R1","first-page":"493","type":"journal-article","volume":"32","author":"V. L. Berezinsky","year":"1971","journal-title":"Sov. Phys. JETP"},{"key":"PhysRevE.111.015305Cc19R2","unstructured":"[Zh. Eksp. Teor. Fiz. 59, 907 (1971)].","type":"other"},{"key":"PhysRevE.111.015305Cc20R1","first-page":"610","type":"journal-article","volume":"34","author":"V. L. Berezinskii","year":"1972","journal-title":"Sov. Phys. JETP"},{"key":"PhysRevE.111.015305Cc21R1","doi-asserted-by":"publisher","DOI":"10.1088\/0022-3719\/6\/7\/010","type":"journal-article"},{"key":"PhysRevE.111.015305Cc22R1","doi-asserted-by":"publisher","DOI":"10.1088\/0022-3719\/7\/6\/005","type":"journal-article"},{"key":"PhysRevE.111.015305Cc23R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.57.6377","type":"journal-article"},{"key":"PhysRevE.111.015305Cc24R1","first-page":"1","type":"journal-article","volume":"21","author":"B. Bloem-Reddy","year":"2020","journal-title":"J. Mach. Learn. Res."},{"key":"PhysRevE.111.015305Cc25R1","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(95)00075-3","type":"journal-article"},{"key":"PhysRevE.111.015305Cc26R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.58.86","type":"journal-article"},{"key":"PhysRevE.111.015305Cc27R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.62.361","type":"journal-article"},{"key":"PhysRevE.111.015305Cc28R1","doi-asserted-by":"crossref","DOI":"10.1561\/9781680836233","type":"book","volume-title":"An Introduction to Variational Autoencoders","author":"D.\u00a0P. Kingma","year":"2019"},{"key":"PhysRevE.111.015305Cc29R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.100.125159","type":"journal-article"},{"key":"PhysRevE.111.015305Cc30R1","unstructured":"github.com\/BrandonWillnecker.","type":"other"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/PhysRevE.111.015305","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/PhysRevE.111.015305\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T18:09:06Z","timestamp":1790705346000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/PhysRevE.111.015305"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,21]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"URL":"https:\/\/doi.org\/10.1103\/physreve.111.015305","relation":{},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,21]]},"assertion":[{"value":"2024-06-19","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"\u00a92025 American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"015305"}}