Gardner physics in amorphous solids and beyond

Berthier, Ludovic; Biroli, Giulio; Charbonneau, Patrick; Corwin, Eric I.; Franz, Silvio; Zamponi, Francesco

doi:10.1063/1.5097175

Cited by 68 publications

(67 citation statements)

References 168 publications

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“…It is well known that in other mean-field modes like the Ising p-spin model, the Potts glass or even spherical models with mixtures of multibody interactions [27], when metastable states are followed down in temperature, bifurcations are encountered. This result leads to the glass-to-glass Gardner phase transition, which has received much attention recently [38].…”

Section: Setting the Stagementioning

confidence: 99%

“…We choose fðqÞ as a polynomial such that the model has a RFOT in thermodynamics, associated with an ideal mode-coupling transition in equilibrium dynamics. In addition, we exclude from our analysis models that can present a Gardner transition [38] to a continuous replica symmetry-breaking state. It is well known that a sufficient condition for this transition is that the function f is such that 1= ffiffiffiffiffiffiffiffiffiffiffi f 00 ðqÞ p is a convex function of q, a property that we assume throughout the paper.…”

Section: Model Definitionmentioning

confidence: 99%

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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

2020

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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.

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Section: Setting the Stagementioning

confidence: 99%

Section: Model Definitionmentioning

confidence: 99%

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

2020

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“…ever longer plateaus at ever greater length scales. In the thermodynamic limit, this series of discrete plateaus will merge into a continuous logarithmic growth of the MSD (7,8).…”

Section: Physicsmentioning

confidence: 99%

“…A snapshot of the configuration of molecules in a glass appears to be the same as that of a dense liquid, and yet glasses are solids not liquids. The recently proposed replica theory of glasses has overcome this lack of a structural signature and provides a first-principles theory (1)(2)(3)(4)(5)(6)(7)(8). This theory predicts two distinct glass phases: a stable glass phase, characterized by an energy landscape of multiple disconnected local minima, and a marginal glass phase, characterized by an energy landscape of basins broken into subbasins, which are themselves broken into subbasins, ad infinitum.…”

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confidence: 99%

Experimental observation of the marginal glass phase in a colloidal glass

Hammond

Corwin

2020

Proc. Natl. Acad. Sci. U.S.A.

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The replica theory of glasses predicts that in the infinite dimensional mean field limit, there exist two distinct glassy phases of matter: stable glass and marginal glass. We have developed a technique to experimentally probe these phases of matter using a colloidal glass. We avoid the difficulties inherent in measuring the long time behavior of glasses by instead focusing on the very short time dynamics of the ballistic to caged transition. We track a single tracer particle within a slowly densifying glass and measure the resulting mean squared displacement (MSD). By analyzing the MSD, we find that upon densification, our colloidal system moves through several states of matter. At lowest densities, it is a subdiffusive liquid. Next, it behaves as a stable glass, marked by the appearance of a plateau in the MSD whose magnitude shrinks with increasing density. However, this shrinking plateau does not shrink to zero; instead, at higher densities, the system behaves as a marginal glass, marked by logarithmic growth in the MSD toward that previous plateau value. Finally, at the highest experimental densities, the system returns to the stable glass phase. This provides direct experimental evidence for the existence of a marginal glass in three dimensions.

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“…There has been recently much interest in Gardner transitions in structural glasses, which is reviewed in Ref. [12].…”

Section: Introductionmentioning

confidence: 99%

Possible instability of one-step replica symmetry breaking in p -spin Ising models outside mean-field theory

Yeo

Moore

2020

Phys. Rev. E

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The fully-connected Ising p-spin model has for p > 2 a discontinuous phase transition from the paramagnetic phase to a stable state with one-step replica symmetry breaking (1RSB). However, simulations in three dimension do not look like these mean-field results and have features more like those which would arise with full replica symmetry breaking (FRSB). To help understand how this might come about we have studied in the fully connected p-spin model the state of two-step replica symmetry breaking (2RSB). It has a free energy degenerate with that of 1RSB, but the weight of the additional peak in P (q) vanishes. We expect that the state with full replica symmetry breaking (FRSB) is also degenerate with that of 1RSB. We suggest that finite size effects will give a nonvanishing weight to the FRSB features, as also will fluctuations about the mean-field solution. Our conclusion is that outside the fully connected model in the thermodynamic limit, FRSB is to be expected rather than 1RSB. arXiv:1911.02719v2 [cond-mat.dis-nn]

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Gardner physics in amorphous solids and beyond

Cited by 68 publications

References 168 publications

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

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

Experimental observation of the marginal glass phase in a colloidal glass

Possible instability of one-step replica symmetry breaking in p -spin Ising models outside mean-field theory

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