{"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/effective-ergodicity-in-single-spin-flip","title":"Effective ergodicity in single-spin-flip dynamics","arxiv_id":"1405.4497","date":"2014-05-18","proceeding":null,"authors":["Mehmet Süzen"],"abstract":"A quantitative measure of convergence to effective ergodicity, the Thirumalai-Mountain (TM) metric, is applied to Metropolis and Glauber single-spin-flip dynamics. In computing this measure, finite lattice ensemble averages are obtained using the exact solution for a one dimensional Ising model, whereas the time averages are computed with Monte Carlo simulations. The time evolution of the effective ergodic convergence of Ising magnetization is monitored. By this approach, diffusion regimes of the effective ergodic convergence of magnetization are identified for different lattice sizes, nonzero temperature, and nonzero external field values. Results show that caution should be taken when using the TM metric at system parameters that give rise to strong correlations.","url_abs":"https://arxiv.org/abs/1405.4497v3","url_pdf":"https://arxiv.org/pdf/1405.4497v3.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":"effective-ergodicity-in-single-spin-flip","repo_url":"https://cran.r-project.org/web/packages/isingLenzMC/index.html","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}