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  • 标题:Strong ergodicity breaking in aging of mean-field spin glasses
  • 本地全文:下载
  • 作者:Massimo Bernaschi ; Alain Billoire ; Andrea Maiorano
  • 期刊名称:Proceedings of the National Academy of Sciences
  • 印刷版ISSN:0027-8424
  • 电子版ISSN:1091-6490
  • 出版年度:2020
  • 卷号:117
  • 期号:30
  • 页码:17522-17527
  • DOI:10.1073/pnas.1910936117
  • 出版社:The National Academy of Sciences of the United States of America
  • 摘要:Out-of-equilibrium relaxation processes show aging if they become slower as time passes. Aging processes are ubiquitous and play a fundamental role in the physics of glasses and spin glasses and in other applications (e.g., in algorithms minimizing complex cost/loss functions). The theory of aging in the out-of-equilibrium dynamics of mean-field spin glass models has achieved a fundamental role, thanks to the asymptotic analytic solution found by Cugliandolo and Kurchan. However, this solution is based on assumptions (e.g., the weak ergodicity breaking hypothesis) which have never been put under a strong test until now. In the present work, we present the results of an extraordinary large set of numerical simulations of the prototypical mean-field spin glass models, namely the Sherrington–Kirkpatrick and the Viana–Bray models. Thanks to a very intensive use of graphics processing units (GPUs), we have been able to run the latter model for more than 2 64 spin updates and thus safely extrapolate the numerical data both in the thermodynamical limit and in the large times limit. The measurements of the two-times correlation functions in isothermal aging after a quench from a random initial configuration to a temperature T < T c provides clear evidence that, at large times, such correlations do not decay to zero as expected by assuming weak ergodicity breaking. We conclude that strong ergodicity breaking takes place in mean-field spin glasses aging dynamics which, asymptotically, takes place in a confined configurational space. Theoretical models for the aging dynamics need to be revised accordingly.
  • 关键词:spin glasses ; phase transitions ; off-equilibrium dynamics
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