Crossover effects on the phase transitions phenomena translated by arborecences and spectral properties

Crossover effects on the phase transitions phenomena translated by arborecences and spectral properties | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Crossover effects on the phase transitions phenomena translated by arborecences and spectral properties Roberto da Silva This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9152966/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 14 You are reading this latest preprint version Abstract This study investigates how visibility graphs constructed from MonteCarlo Markov Chain time series of spin models capture the critical behavior of the system. More precisely, we show that this approach identifies continuous phase transitions as well as important nuances, such as crossover effects occurring in the transition from a critical line to a first-order line through a tricritical point, as observed, for example, in the Blume--Emery--Griffiths model or, in a simpler setting, in the Blume--Capel model. By applying Kirchhoff's theorem, we show that the number of spanning trees of the resulting graphs serves as a sensitive indicator of these phase transitions. Furthermore, a qualitative analysis of the adjacency matrices based on random matrix theory provides additional evidence for these phenomena. The methodology developed here can potentially be extended to the analysis of criticality in empirical time series from complex systems, such as climate, financial, and epidemiological data, where the Hamiltonian governing the dynamics is not necessarily known. Physical sciences/Chemistry Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 18 May, 2026 Reviews received at journal 17 May, 2026 Reviewers agreed at journal 15 May, 2026 Reviewers agreed at journal 14 May, 2026 Reviewers agreed at journal 13 May, 2026 Reviewers agreed at journal 17 Apr, 2026 Reviews received at journal 03 Apr, 2026 Reviewers agreed at journal 24 Mar, 2026 Reviewers agreed at journal 24 Mar, 2026 Reviewers invited by journal 24 Mar, 2026 Editor invited by journal 24 Mar, 2026 Editor assigned by journal 20 Mar, 2026 Submission checks completed at journal 20 Mar, 2026 First submitted to journal 17 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9152966","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":611605907,"identity":"2edcc64a-03f8-49ec-8cdd-bf58f77c49c8","order_by":0,"name":"Roberto da Silva","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYFCCBCAqYGDgZ2Z8wMBgAxLhIUaLAQODZDMzkEwjVgsDULHBAWK1mLcnP/7wwOCwvPFxZgZmnoR7dvMbeI99wKdF5swzM4kEg8OG2w6DtRQnbzjAlzwDnxYJiQQzoF/SGLcd5j/AzPsjIdmAgccYr8MkJNI/fwBqsd/cDLYlIVm+gaCWHAOgw2wSNzBDtNgxHCCkhedNGUhL8gygXw7OSUgA+osvGb8W9vTNH39USNj29x9mfPAmIcFevr33MF4tKOAAECc2MBOvAQLsSdUwCkbBKBgFwx8AALtJQHcEi1pUAAAAAElFTkSuQmCC","orcid":"","institution":"Federal University of Rio Grande do Sul","correspondingAuthor":true,"prefix":"","firstName":"Roberto","middleName":"da","lastName":"Silva","suffix":""}],"badges":[],"createdAt":"2026-03-17 23:53:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9152966/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9152966/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105566579,"identity":"d4d8008d-14f6-4c83-9e6f-d3a8d30065c4","added_by":"auto","created_at":"2026-03-27 12:56:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":775888,"visible":true,"origin":"","legend":"","description":"","filename":"treescrossover.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9152966/v1_covered_02342fb1-08c6-433d-8d04-5a18347ac2ba.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Crossover effects on the phase transitions phenomena translated by arborecences and spectral properties","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9152966/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9152966/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study investigates how visibility graphs constructed from MonteCarlo Markov Chain time series of spin models capture the critical behavior of the system. 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