{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T22:05:50Z","timestamp":1790719550463,"version":"4.1.0"},"reference-count":75,"publisher":"American Physical Society (APS)","issue":"2","license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-license"}],"funder":[{"DOI":"10.13039\/501100018877","name":"Research and Innovation Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100018877","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2025,7,30]]},"DOI":"10.1103\/d1y6-b8hs","type":"journal-article","created":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T12:01:54Z","timestamp":1753876914000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Critical dynamics of three-dimensional\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:msub>\n                        <mml:mi mathvariant=\"double-struck\">Z<\/mml:mi>\n                        <mml:mi>N<\/mml:mi>\n                      <\/mml:msub>\n                    <\/mml:math>\n                    gauge models and the inverted\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <mml:mrow>\n                        <mml:mi>X<\/mml:mi>\n                        <mml:mi>Y<\/mml:mi>\n                      <\/mml:mrow>\n                    <\/mml:math>\n                    universality class"],"prefix":"10.1103","volume":"112","author":[{"given":"Claudio","family":"Bonati","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03ad39j10","id-type":"ROR","asserted-by":"publisher"}],"name":"Dipartimento di Fisica dell'Universit\u00e0 di Pisa"},{"id":[{"id":"https:\/\/ror.org\/05symbg58","id-type":"ROR","asserted-by":"publisher"}],"name":"INFN"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9355-6064","authenticated-orcid":true,"given":"Haralambos","family":"Panagopoulos","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02qjrjx09","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Cyprus"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7469-9614","authenticated-orcid":true,"given":"Ettore","family":"Vicari","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03ad39j10","id-type":"ROR","asserted-by":"publisher"}],"name":"Dipartimento di Fisica dell'Universit\u00e0 di Pisa"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"d1y6-b8hsCc1R1","volume-title":"The Quantum Theory of Fields. Volume I. Foundations","author":"S. Weinberg","year":"2005","type":"book"},{"key":"d1y6-b8hsCc1R2","volume-title":"The Quantum Theory of Fields. Volume II. Modern Applications","year":"2005","type":"book"},{"key":"d1y6-b8hsCc2R1","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198509233.001.0001","type":"book","volume-title":"Quantum Field Theory and Critical Phenomena","author":"J. Zinn-Justin","year":"2002"},{"key":"d1y6-b8hsCc3R1","volume-title":"Basic Notions of Condensed Matter Physics","author":"P.\u00a0W. Anderson","year":"1984","type":"book"},{"key":"d1y6-b8hsCc4R1","volume-title":"Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons","author":"X.-G. Wen","year":"2004","type":"book"},{"key":"d1y6-b8hsCc5R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139015509","type":"book","volume-title":"Field Theories of Condensed Matter Physics","author":"E. Fradkin","year":"2013"},{"key":"d1y6-b8hsCc6R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6633\/aae110","type":"journal-article"},{"key":"d1y6-b8hsCc7R1","doi-asserted-by":"crossref","DOI":"10.1017\/9781009212717","type":"book","volume-title":"Quantum Phases of Matter","author":"S. Sachdev","year":"2023"},{"key":"d1y6-b8hsCc8R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2025.05.004","type":"journal-article"},{"key":"d1y6-b8hsCc9R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1665530","type":"journal-article"},{"key":"d1y6-b8hsCc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.51.659","type":"journal-article"},{"key":"d1y6-b8hsCc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.19.3682","type":"journal-article"},{"key":"d1y6-b8hsCc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.52.453","type":"journal-article"},{"key":"d1y6-b8hsCc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.47.1556","type":"journal-article"},{"key":"d1y6-b8hsCc14R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.67.014525","type":"journal-article"},{"key":"d1y6-b8hsCc15R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.65.165112","type":"journal-article"},{"key":"d1y6-b8hsCc16R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.023031","type":"journal-article"},{"key":"d1y6-b8hsCc17R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.109.044146","type":"journal-article"},{"key":"d1y6-b8hsCc18R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.034517","type":"journal-article"},{"key":"d1y6-b8hsCc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.55.583","type":"journal-article"},{"key":"d1y6-b8hsCc20R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.47.543","type":"journal-article"},{"key":"d1y6-b8hsCc21R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(02)00219-3","type":"journal-article"},{"key":"d1y6-b8hsCc22R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2021.08.003","type":"journal-article"},{"key":"d1y6-b8hsCc23R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.74.144506","type":"journal-article"},{"key":"d1y6-b8hsCc24R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.100.224517","type":"journal-article"},{"key":"d1y6-b8hsCc25R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP06(2020)142","type":"journal-article"},{"key":"d1y6-b8hsCc26R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.103.085104","type":"journal-article"},{"key":"d1y6-b8hsCc27R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.32.292","type":"journal-article"},{"key":"d1y6-b8hsCc28R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.76.4588","type":"journal-article"},{"key":"d1y6-b8hsCc29R1","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/29\/13\/014","type":"journal-article"},{"key":"d1y6-b8hsCc30R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.53.5734","type":"journal-article"},{"key":"d1y6-b8hsCc31R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.1964","type":"journal-article"},{"key":"d1y6-b8hsCc32R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.84.3426","type":"journal-article"},{"key":"d1y6-b8hsCc33R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.88.232001","type":"journal-article"},{"key":"d1y6-b8hsCc34R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.65.104501","type":"journal-article"},{"key":"d1y6-b8hsCc35R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511755521","type":"book","volume-title":"A Modern Approach to Critical Phenomena","author":"I. Herbut","year":"2007"},{"key":"d1y6-b8hsCc36R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.108.044125","type":"journal-article"},{"key":"d1y6-b8hsCc37R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.49.435","type":"journal-article"},{"key":"d1y6-b8hsCc38R1","volume-title":"Modern Theory of Critical Phenomena","author":"S.-K. Ma","year":"2001","type":"book"},{"key":"d1y6-b8hsCc39R1","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/24\/R01","type":"journal-article"},{"key":"d1y6-b8hsCc40R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.111.115129","type":"journal-article"},{"key":"d1y6-b8hsCc41R1","first-page":"483","type":"journal-article","volume":"24","author":"G. Parisi","year":"1981","journal-title":"Sci. Sin."},{"key":"d1y6-b8hsCc42R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(81)90202-9","type":"journal-article"},{"key":"d1y6-b8hsCc43R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(83)90240-7","type":"journal-article"},{"key":"d1y6-b8hsCc44R1","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.70.298","type":"journal-article"},{"key":"d1y6-b8hsCc45R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(86)90592-4","type":"journal-article"},{"key":"d1y6-b8hsCc46R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(88)90358-6","type":"journal-article"},{"key":"d1y6-b8hsCc47R1","doi-asserted-by":"publisher","DOI":"10.5488\/CMP.10.2.189","type":"journal-article"},{"key":"d1y6-b8hsCc48R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.92.097004","type":"journal-article"},{"key":"d1y6-b8hsCc49R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.88.137004","type":"journal-article"},{"key":"d1y6-b8hsCc50R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.87.197003","type":"journal-article"},{"key":"d1y6-b8hsCc51R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.61.15412","type":"journal-article"},{"key":"d1y6-b8hsCc52R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.58.2827","type":"journal-article"},{"key":"d1y6-b8hsCc53R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.78.2620","type":"journal-article"},{"key":"d1y6-b8hsCc54R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.66.3071","type":"journal-article"},{"key":"d1y6-b8hsCc55R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(93)90502-G","type":"journal-article"},{"key":"d1y6-b8hsCc57R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02765532","type":"journal-article"},{"key":"d1y6-b8hsCc58R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.111.054107","type":"journal-article"},{"key":"d1y6-b8hsCc59R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.97.024432","type":"journal-article"},{"key":"d1y6-b8hsCc60R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01020288","type":"journal-article"},{"key":"d1y6-b8hsCc61R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.022126","type":"journal-article"},{"key":"d1y6-b8hsCc62R1","volume-title":"Phase Transitions and Critical Phenomena","author":"K. Binder","year":"1976","type":"book"},{"key":"d1y6-b8hsCc63R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.109.064107","type":"journal-article"},{"key":"d1y6-b8hsCc64R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2022.127530","type":"journal-article"},{"key":"d1y6-b8hsCc65R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01018251","type":"journal-article"},{"key":"d1y6-b8hsCc66R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.29.1548","type":"journal-article"},{"key":"d1y6-b8hsCc67R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2013.12.003","type":"journal-article"},{"key":"d1y6-b8hsCc68R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(78)90207-9","type":"journal-article"},{"key":"d1y6-b8hsCc69R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.052148","type":"journal-article"},{"key":"d1y6-b8hsCc70R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.29.306","type":"journal-article"},{"key":"d1y6-b8hsCc71R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(86)90282-8","type":"journal-article"},{"key":"d1y6-b8hsCc72R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.457480","type":"journal-article"},{"key":"d1y6-b8hsCc73R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0010-4655(03)00467-3","type":"journal-article"},{"key":"d1y6-b8hsCc74R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2004.05.038","type":"journal-article"},{"key":"d1y6-b8hsCc75R1","doi-asserted-by":"crossref","unstructured":"A.\u00a0D. Sokal, Monte Carlo methods in statistical mechanics: Foundations and new algorithms, in Functional Integration. Basics and Applications, edited by C. DeWitt-Morette, P. Cartier, and A. Folacci (Springer, New York, 1997), p. 131.","DOI":"10.1007\/978-1-4899-0319-8_6","type":"book"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/d1y6-b8hs","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/d1y6-b8hs\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T21:23:20Z","timestamp":1790717000000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/d1y6-b8hs"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,19]]},"references-count":75,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,8]]}},"URL":"https:\/\/doi.org\/10.1103\/d1y6-b8hs","relation":{},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,19]]},"assertion":[{"value":"2025-05-16","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":"024125"}}