scholarly journals Spectral Gap Estimates in Mean Field Spin Glasses

2018 ◽  
Vol 361 (1) ◽  
pp. 1-52 ◽  
Author(s):  
Gérard Ben Arous ◽  
Aukosh Jagannath
Keyword(s):  
Spin Glasses ◽  
Spectral Gap ◽  
Mean Field ◽  
Mean Field Spin Glasses

scholarly journals Nonrealistic Behavior of Mean-Field Spin Glasses

2003 ◽  
Vol 91 (19) ◽  
Author(s):  
C. M. Newman ◽  
D. L. Stein
Keyword(s):  
Spin Glasses ◽  
Mean Field ◽  
Mean Field Spin Glasses

scholarly journals Universality of the REM for Dynamics of Mean-Field Spin Glasses

2008 ◽  
Vol 282 (3) ◽  
pp. 663-695 ◽  
Author(s):  
Gérard Ben Arous ◽  
Anton Bovier ◽  
Jiří Černý
Keyword(s):  
Spin Glasses ◽  
Mean Field ◽  
Mean Field Spin Glasses

scholarly journals Universality in bipartite mean field spin glasses

2012 ◽  
Vol 53 (12) ◽  
pp. 123304 ◽  
Author(s):  
Giuseppe Genovese
Keyword(s):  
Spin Glasses ◽  
Mean Field ◽  
Mean Field Spin Glasses

scholarly journals Universal structures in some mean field spin glasses and an application

2008 ◽  
Vol 49 (12) ◽  
pp. 125205 ◽  
Author(s):  
Erwin Bolthausen ◽  
Nicola Kistler
Keyword(s):  
Spin Glasses ◽  
Mean Field ◽  
Mean Field Spin Glasses

scholarly journals Strong ergodicity breaking in aging of mean-field spin glasses

2020 ◽  
Vol 117 (30) ◽  
pp. 17522-17527
Author(s):  
Massimo Bernaschi ◽  
Alain Billoire ◽  
Andrea Maiorano ◽  
Giorgio Parisi ◽  
Federico Ricci-Tersenghi
Keyword(s):  
Spin Glass ◽  
Spin Glasses ◽  
Mean Field ◽  
Relaxation Processes ◽  
Large Set ◽  
Weak Ergodicity ◽  
Strong Ergodicity ◽  
Weak Ergodicity Breaking ◽  
Ergodicity Breaking ◽  
Mean Field Spin Glasses

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 than264spin 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 temperatureT<Tcprovides 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.

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