Single replica spin-glass phase detection using field variation and machine learning

Single replica spin-glass phase detection using field variation and machine learning | 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 Single replica spin-glass phase detection using field variation and machine learning Ali Talebi, Mahsa Bagherikalhor, Behrouz Askari, G.Reza Jafari This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5861315/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The Sherrington-Kirkpatrick (SK) spin-glass model exhibits well-studied phase transitions that are mostly established using replica-based methods. Regardless of the method used for detection, the intrinsic phase of a system exists whether or not replicas are considered. Therefore, in this study, we propose a novel method for phase detection based on the variation of the local field experienced by each spin in a configuration of a single replica. The mean and the variance of these local fields are powerful indicators that effectively distinguish different phases, including ferromagnetic, paramagnetic, and spin-glass phases. By analyzing the mean and variance of these local fields, we develop a machine learning algorithm to generate the phase diagram, which shows strong agreement with the theoretical solutions for the Sherrington-Kirkpatrick model. Also, this algorithm offers a more computationally efficient approach for phase detection in spin-glass systems. Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Statistical physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-5861315","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":449869075,"identity":"0eab2bd3-8f31-419f-acfc-0cca0469934f","order_by":0,"name":"Ali Talebi","email":"","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":false,"prefix":"","firstName":"Ali","middleName":"","lastName":"Talebi","suffix":""},{"id":449869076,"identity":"bba68ceb-dc50-4ebd-84c6-7b226f31ebce","order_by":1,"name":"Mahsa Bagherikalhor","email":"","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":false,"prefix":"","firstName":"Mahsa","middleName":"","lastName":"Bagherikalhor","suffix":""},{"id":449869077,"identity":"2f839d95-aec7-4597-b955-7a06a0ed7e8e","order_by":2,"name":"Behrouz Askari","email":"","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":false,"prefix":"","firstName":"Behrouz","middleName":"","lastName":"Askari","suffix":""},{"id":449869078,"identity":"7d415a1b-5c72-4022-9bbe-5cfcb920bd98","order_by":3,"name":"G.Reza Jafari","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIie3RoQvCQBTH8Z/lLA+tJ4r7FybCME3/lCcHJrFYDIalJdF/6a0sTaxLit2wJCbxxGDzZhO8b7oH9+EdHODz/WaMFUBt0GtUtUhhSSf5guBJEArVfFUwwbmS9bE3POxzjXWMVlc+k4HAaMmXFJWLmUZuoFrsIAm4Wym2hCINJVCuB1pibnJnGu4KS+41SADMdJYyhZhHupHWIKElo2zLpMuFGU23htxbEjKlXHnc3u2zsrrG/WDj2nK68HuyR/fvBElTnJd8Pp/vz3sAYOY5/THOBYIAAAAASUVORK5CYII=","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":true,"prefix":"","firstName":"G.Reza","middleName":"","lastName":"Jafari","suffix":""}],"badges":[],"createdAt":"2025-01-19 21:08:04","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5861315/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5861315/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82912816,"identity":"b7d4939a-ba1d-49fb-a85f-fd246ee46d14","added_by":"auto","created_at":"2025-05-16 15:31:41","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3130825,"visible":true,"origin":"","legend":"","description":"","filename":"SinglereplicaspinglassphasedetectionusingfieldvariationandmachinelearningV2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5861315/v1_covered_2f5dbb99-02b1-4a99-9ab1-7159809d6733.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Single replica spin-glass phase detection using field variation and machine learning","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5861315/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5861315/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The Sherrington-Kirkpatrick (SK) spin-glass model exhibits well-studied phase transitions that are mostly established using replica-based methods. 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