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- W3080452121 abstract "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.25 MoreReceived 6 January 2020Revised 19 May 2020Accepted 30 June 2020DOI:https://doi.org/10.1103/PhysRevX.10.031045Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsTechniquesDissipative particle dynamicsReplica theoryStatistical Physics" @default.
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- W3080452121 date "2020-08-25" @default.
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- W3080452121 title "Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>p</mml:mi></mml:math> -Spin Model" @default.
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- W3080452121 doi "https://doi.org/10.1103/physrevx.10.031045" @default.
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