Depinning of KPZ Interfaces in Fractional Brownian Landscapes

Depinning of KPZ Interfaces in Fractional Brownian Landscapes | 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 Depinning of KPZ Interfaces in Fractional Brownian Landscapes Neda Valizadeh, Mortaza Nattagh Najafi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8933582/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Apr, 2026 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract We explore the critical dynamics of driven interfaces propagating through a two-dimensional disordered medium with long-range spatial correlations, modeled using fractional Brownian motion (FBM). Departing from conventional models with uncorrelated disorder, we introduce quenched noise fields characterized by a tunable Hurst exponent ( H ), allowing systematic control over the spatial structure of the background medium. The interface evolution is governed by a quenched Kardar–Parisi–Zhang (QKPZ) equation modified to account for correlated disorder, namely QKPZ$_H$. Through analytical scaling analysis, we uncover how the presence of long-range correlations reshapes the depinning transition, alters the critical force ( F_c ), and gives rise to a family of critical exponents that depend continuously on ( H ). Our findings reveal a rich interplay between disorder correlations and the non-linearity term in QKPZ$_H$, leading to a breakdown of conventional universality and the emergence of nontrivial scaling behaviors. The exponents are found to change by $H$ in the anticorrelation regime ($H0.5$), suggesting a super-universal behavior for the latter. By a comparison with the quenched Edwards-Wilkinson model, we study the effect of the non-linearity term in the QKPZ$_H$ model. This work provides new insights into the physics of driven systems in complex environments and paves the way for understanding transport in correlated disordered media. Physical sciences/Materials science Physical sciences/Mathematics and computing Physical sciences/Physics KPZ Interfaces Depinning transition Fractional Brownian motion Long-range correlations Interface dynamics Critical exponents Non-equilibrium statistical physics Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryMaterial.pdf Cite Share Download PDF Status: Published Journal Publication published 27 Apr, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 01 Apr, 2026 Reviews received at journal 01 Apr, 2026 Reviewers agreed at journal 01 Apr, 2026 Reviews received at journal 24 Mar, 2026 Reviewers agreed at journal 14 Mar, 2026 Reviewers invited by journal 26 Feb, 2026 Editor invited by journal 26 Feb, 2026 Editor assigned by journal 24 Feb, 2026 Submission checks completed at journal 24 Feb, 2026 First submitted to journal 21 Feb, 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. 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-8933582","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":598325961,"identity":"f3255ff4-301e-4b2d-9835-a74114aa4292","order_by":0,"name":"Neda Valizadeh","email":"","orcid":"","institution":"Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179,","correspondingAuthor":false,"prefix":"","firstName":"Neda","middleName":"","lastName":"Valizadeh","suffix":""},{"id":598325962,"identity":"8a204887-984e-4ed2-8576-f99184bb0e0d","order_by":1,"name":"Mortaza Nattagh Najafi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBUlEQVRIiWNgGAWjYAiAA3Jg8gF+VYwNEJoZxDhgDNaSQIqWRDAPnxbd9t7nDz78sWMwZz9//MGPX3fS54cdfgi0xU5OtwG7FrMzxw0bZ/AkM1j2JDM29vY9y914O80AqCXZ2OwADi030hibeSSYGQwOJDM28PYczt04OwGk5UDiNnxa/hjUMxicf8zY+LfncLrh7PQPhLUwJBxmMLiRDLTux+EEeekcAracOcY4s+fAcR6DG48NZ8s2HDbcIJ1TcCDBAI9fjrcxfPjxp1rO4Hzig49v/hyWl5+dvvnDhwo7OVxaYIAHTDK2MQDDAcQywK8cCfxhYJBvIFr1KBgFo2AUjBAAAGIYa5YwVMfVAAAAAElFTkSuQmCC","orcid":"","institution":"Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179,","correspondingAuthor":true,"prefix":"","firstName":"Mortaza","middleName":"Nattagh","lastName":"Najafi","suffix":""}],"badges":[],"createdAt":"2026-02-21 12:53:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8933582/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8933582/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-026-50838-y","type":"published","date":"2026-04-27T15:57:30+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":108439281,"identity":"88f7f04a-eb3e-4b0c-9baa-c89b6a965133","added_by":"auto","created_at":"2026-05-04 16:19:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":604361,"visible":true,"origin":"","legend":"","description":"","filename":"DepinningofKPZInterfacesinFractionalBrownianLandscapes.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8933582/v1_covered_caee7454-e623-43f0-ab68-6944e4e12e5a.pdf"},{"id":103822087,"identity":"031c9be4-f5f7-4c9c-bf19-d42783b8963f","added_by":"auto","created_at":"2026-03-03 10:31:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":100326,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterial.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8933582/v1/82e7d1f0b2bd1fd7d5f5be92.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Depinning of KPZ Interfaces in Fractional Brownian Landscapes","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"KPZ Interfaces, Depinning transition, Fractional Brownian motion, Long-range correlations, Interface dynamics, Critical exponents, Non-equilibrium statistical physics","lastPublishedDoi":"10.21203/rs.3.rs-8933582/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8933582/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We explore the critical dynamics of driven interfaces propagating through a two-dimensional disordered medium with long-range spatial correlations, modeled using fractional Brownian motion (FBM). Departing from conventional models with uncorrelated disorder, we introduce quenched noise fields characterized by a tunable Hurst exponent \\( H \\), allowing systematic control over the spatial structure of the background medium. The interface evolution is governed by a quenched Kardar–Parisi–Zhang (QKPZ) equation modified to account for correlated disorder, namely QKPZ$_H$. Through analytical scaling analysis, we uncover how the presence of long-range correlations reshapes the depinning transition, alters the critical force \\( F_c \\), and gives rise to a family of critical exponents that depend continuously on \\( H \\). Our findings reveal a rich interplay between disorder correlations and the non-linearity term in QKPZ$_H$, leading to a breakdown of conventional universality and the emergence of nontrivial scaling behaviors. The exponents are found to change by $H$ in the anticorrelation regime ($H\u003c0.5$), while they are nearly constant in the correlation regime ($H\u003e0.5$), suggesting a super-universal behavior for the latter. By a comparison with the quenched Edwards-Wilkinson model, we study the effect of the non-linearity term in the QKPZ$_H$ model. This work provides new insights into the physics of driven systems in complex environments and paves the way for understanding transport in correlated disordered media.","manuscriptTitle":"Depinning of KPZ Interfaces in Fractional Brownian Landscapes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-03 10:31:32","doi":"10.21203/rs.3.rs-8933582/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-01T15:30:12+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-01T12:54:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"283361121932764264610500193784393111921","date":"2026-04-01T12:32:48+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-24T11:19:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"80666259726139922663980461847059175400","date":"2026-03-14T12:30:54+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-26T12:39:16+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-02-26T11:29:19+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-24T11:28:27+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-24T11:27:40+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-02-21T12:46:47+00:00","index":"","fulltext":""}],"status":"published","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}}],"origin":"","ownerIdentity":"2eb5476c-e761-4e08-9872-a598bc2ea7b5","owner":[],"postedDate":"March 3rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":63675554,"name":"Physical sciences/Materials science"},{"id":63675555,"name":"Physical sciences/Mathematics and computing"},{"id":63675556,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-05-04T16:19:22+00:00","versionOfRecord":{"articleIdentity":"rs-8933582","link":"https://doi.org/10.1038/s41598-026-50838-y","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-04-27 15:57:30","publishedOnDateReadable":"April 27th, 2026"},"versionCreatedAt":"2026-03-03 10:31:32","video":"","vorDoi":"10.1038/s41598-026-50838-y","vorDoiUrl":"https://doi.org/10.1038/s41598-026-50838-y","workflowStages":[]},"version":"v1","identity":"rs-8933582","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8933582","identity":"rs-8933582","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}