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Journal Articles Proceedings of the National Academy of Sciences of the United States of America Year : 2020

## Strong ergodicity breaking in aging of mean-field spin glasses

Alain Billoire
• Function : Author
Andrea Maiorano
• Function : Author
Giorgio Parisi
• Function : Author
Federico Ricci-Tersenghi
• Function : Correspondent author
• PersonId : 1095983

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#### Abstract

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 meanfield 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 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 < Tc 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 meanfield spin glasses aging dynamics which, asymptotically, takes place in a confined configurational space. Theoretical models for the aging dynamics need to be revised accordingly

#### Domains

Physics [physics]

### Dates and versions

cea-03197759 , version 1 (14-04-2021)

### Identifiers

• HAL Id : cea-03197759 , version 1
• DOI :

### Cite

Massimo Bernaschi, Alain Billoire, Andrea Maiorano, Giorgio Parisi, Federico Ricci-Tersenghi. Strong ergodicity breaking in aging of mean-field spin glasses. Proceedings of the National Academy of Sciences of the United States of America, 2020, 117 (30), pp.17522-17527. ⟨10.1073/pnas.1910936117⟩. ⟨cea-03197759⟩

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