{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/uniqueness-of-the-thermodynamic-limit-for","title":"Uniqueness of the thermodynamic limit for driven disordered elastic interfaces","arxiv_id":"1308.4329","date":"2013-08-20","proceeding":null,"authors":["A. B. Kolton","S. Bustingorry","E. E. Ferrero","A. Rosso"],"abstract":"We study the finite size fluctuations at the depinning transition for a one-dimensional elastic interface of size $L$ displacing in a disordered medium of transverse size $M=k L^\\zeta$ with periodic boundary conditions, where $\\zeta$ is the depinning roughness exponent and $k$ is a finite aspect ratio parameter. We focus on the crossover from the infinitely narrow ($k\\to 0$) to the infinitely wide ($k\\to \\infty$) medium. We find that at the thermodynamic limit both the value of the critical force and the precise behavior of the velocity-force characteristics are {\\it unique} and $k$-independent. We also show that the finite size fluctuations of the critical force (bias and variance) as well as the global width of the interface cross over from a power-law to a logarithm as a function of $k$. Our results are relevant for understanding anisotropic size-effects in force-driven and velocity-driven interfaces.","url_abs":"https://arxiv.org/abs/1308.4329v1","url_pdf":"https://arxiv.org/pdf/1308.4329v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"uniqueness-of-the-thermodynamic-limit-for","repo_url":"https://bitbucket.org/ezeferrero/qew","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}