Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p-Spin Model

The spherical p-spin model is a fundamental model in statistical mechanics of a disordered system with a random first-order transition. The dynamics of this model is interesting both for the physics of glasses and for its implications on hard optimization problems. Here, we revisit the out-of-equili...

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Autores principales:	Giampaolo Folena, Silvio Franz, Federico Ricci-Tersenghi
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/49b7fb6bbfbb4f1fbf46b3a90bc8d167
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spelling	oai:doaj.org-article:49b7fb6bbfbb4f1fbf46b3a90bc8d1672021-12-02T10:54:32ZRethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p-Spin Model10.1103/PhysRevX.10.0310452160-3308https://doaj.org/article/49b7fb6bbfbb4f1fbf46b3a90bc8d1672020-08-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.031045http://doi.org/10.1103/PhysRevX.10.031045https://doaj.org/toc/2160-3308The spherical p-spin model is a fundamental model in statistical mechanics of a disordered system with a random first-order transition. The dynamics of this model is interesting both for the physics of glasses and for its implications on hard optimization problems. Here, we revisit the out-of-equilibrium dynamics of the spherical mixed p-spin model, which differs from the pure p-spin model by the fact that the Hamiltonian is not a homogeneous function of its variables. We consider quenches (gradient descent dynamics) starting from initial conditions thermalized in the high-temperature ergodic phase. Unexpectedly, we find that, differently from the pure p-spin case, the asymptotic states of the dynamics keep memory of the initial condition. The final energy is a decreasing function of the initial temperature, and the system remains correlated with the initial state. This dependence disproves the idea of a unique “threshold” energy level attracting dynamics starting from high-temperature initial conditions. Thermalization, which could be achieved, e.g., by an algorithm like simulated annealing, provides an advantage in gradient descent dynamics and, last but not least, brings mean-field models closer to real glass phenomenology, where such a dependence is observed in numerical simulations. We investigate the nature of the asymptotic dynamics, finding an aging state that relaxes towards deep, marginally stable minima. However, careful analysis rules out simple generalizations of the aging solution of the pure model. We compute the constrained complexity with the aim of connecting the asymptotic solution to the energy landscape.Giampaolo FolenaSilvio FranzFederico Ricci-TersenghiAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 3, p 031045 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Giampaolo Folena Silvio Franz Federico Ricci-Tersenghi Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p-Spin Model
description	The spherical p-spin model is a fundamental model in statistical mechanics of a disordered system with a random first-order transition. The dynamics of this model is interesting both for the physics of glasses and for its implications on hard optimization problems. Here, we revisit the out-of-equilibrium dynamics of the spherical mixed p-spin model, which differs from the pure p-spin model by the fact that the Hamiltonian is not a homogeneous function of its variables. We consider quenches (gradient descent dynamics) starting from initial conditions thermalized in the high-temperature ergodic phase. Unexpectedly, we find that, differently from the pure p-spin case, the asymptotic states of the dynamics keep memory of the initial condition. The final energy is a decreasing function of the initial temperature, and the system remains correlated with the initial state. This dependence disproves the idea of a unique “threshold” energy level attracting dynamics starting from high-temperature initial conditions. Thermalization, which could be achieved, e.g., by an algorithm like simulated annealing, provides an advantage in gradient descent dynamics and, last but not least, brings mean-field models closer to real glass phenomenology, where such a dependence is observed in numerical simulations. We investigate the nature of the asymptotic dynamics, finding an aging state that relaxes towards deep, marginally stable minima. However, careful analysis rules out simple generalizations of the aging solution of the pure model. We compute the constrained complexity with the aim of connecting the asymptotic solution to the energy landscape.
format	article
author	Giampaolo Folena Silvio Franz Federico Ricci-Tersenghi
author_facet	Giampaolo Folena Silvio Franz Federico Ricci-Tersenghi
author_sort	Giampaolo Folena
title	Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p-Spin Model
title_short	Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p-Spin Model
title_full	Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p-Spin Model
title_fullStr	Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p-Spin Model
title_full_unstemmed	Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p-Spin Model
title_sort	rethinking mean-field glassy dynamics and its relation with the energy landscape: the surprising case of the spherical mixed p-spin model
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/49b7fb6bbfbb4f1fbf46b3a90bc8d167
work_keys_str_mv	AT giampaolofolena rethinkingmeanfieldglassydynamicsanditsrelationwiththeenergylandscapethesurprisingcaseofthesphericalmixedpspinmodel AT silviofranz rethinkingmeanfieldglassydynamicsanditsrelationwiththeenergylandscapethesurprisingcaseofthesphericalmixedpspinmodel AT federicoriccitersenghi rethinkingmeanfieldglassydynamicsanditsrelationwiththeenergylandscapethesurprisingcaseofthesphericalmixedpspinmodel
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Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p-Spin Model

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