Bernaschi Massimo, Billoire Alain, Maiorano Andrea, Parisi Giorgio, Ricci-Tersenghi Federico
Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, 00185 Rome, Italy.
Institut de Physique Théorique, Université Paris Saclay, CNRS, Commissariat à l'énergie atomique et aux énergies alternatives, F-91191, Gif-sur-Yvette, France.
Proc Natl Acad Sci U S A. 2020 Jul 28;117(30):17522-17527. doi: 10.1073/pnas.1910936117. Epub 2020 Jul 10.
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 [Formula: see text] 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 [Formula: see text] 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.
非平衡弛豫过程如果随着时间推移而变慢，则显示出老化现象。老化过程无处不在，在玻璃和自旋玻璃的物理学以及其他应用（例如，在最小化复杂成本/损失函数的算法中）中发挥着重要作用。由于库利亚多洛和库尔尚找到的渐近解析解，平均场自旋玻璃模型的非平衡动力学中的老化理论发挥了重要作用。然而，这个解是基于一些假设（例如，弱遍历性破坏假设），直到现在这些假设从未受到过严格检验。在本工作中，我们展示了对典型平均场自旋玻璃模型，即谢林顿 - 柯克帕特里克模型和维亚纳 - 布雷模型进行的大量数值模拟结果。由于非常密集地使用了图形处理单元（GPU），我们得以对后一个模型运行超过[公式：见原文]次自旋更新，从而能够在热力学极限和长时间极限下安全地外推数值数据。从随机初始构型淬火到温度[公式：见原文]后，在等温老化过程中对双时关联函数的测量提供了明确证据，即在长时间时，这种关联并不像假设弱遍历性破坏时预期的那样衰减到零。我们得出结论，在平均场自旋玻璃老化动力学中发生了强遍历性破坏，渐近地，这种破坏发生在一个受限的构型空间中。老化动力学的理论模型需要相应地进行修订。
