A general approach to systems with randomly pinned particles: unfolding and clarifying the Random Pinning Glass Transition

Pinning a fraction of particles from an equilibrium configuration in supercooled liquids has been recently proposed as a way to induce a new kind of glass transition, the Random Pinning Glass Transition (RPGT). The RPGT has been predicted to share some features of standard thermodynamic glass transitions and usual first order ones. Thanks to its special nature, the approach and the study of the RPGT appears to be a fairly reachable task compared to the daunting problem of inspecting standard glass transitions. In this Letter we generalize the pinning particle procedure. We study a mean-field system where the pinned configuration is extracted from the equilibrium distribution at temperature $T'$ and the thermodynamics of the non pinned particles is observed at a lower temperature $T$. A more complicated physics emerges from this generalization eventually clarifying the origin and the peculiar characteristics of the RPGT.Comment: 7 pages, 1 figur

Fluctuations and shape of cooperative rearranging regions in glass-forming liquids

We develop a theory of amorphous interfaces in glass-forming liquids. We show that the statistical properties of these surfaces, which separate regions characterized by different amorphous arrangements of particles, coincide with the ones of domain walls in the random field Ising model. A major consequence of our results is that supercooled liquids are characterized by two different static lengths: the point-to-set ξPS, which is a measure of the spatial extent of cooperative rearranging regions, and the wandering length ξ⊥, which is related to the fluctuations of their shape. We find that ξ⊥ grows when approaching the glass transition but slower than ξPS. The wandering length increases as s−1/2c, where sc is the configurational entropy. Our results strengthen the relationship with the random field Ising model found in recent works. They are in agreement with previous numerical studies of amorphous interfaces and provide a theoretical framework for explaining numerical and experimental findings on pinned particle systems and static lengths in glass-forming liquids

Numerical evidences of universal trap-like aging dynamics

Trap models have been initially proposed as toy models for dynamical relaxation in extremely simplified rough potential energy landscapes. Their importance has considerably grown recently thanks to the discovery that the trap like aging mechanism is directly controlling the out-of-equilibrium relaxation processes of more sophisticated spin models, that are considered as the solvable counterpart of real disordered systems. Establishing on a firmer ground the connection between these spin model out-of-equilibrium behavior and the trap like aging mechanism would shed new light on the properties, still largely mysterious, of the activated out-of-equilibrium dynamics of disordered systems. In this work we discuss numerical evidences of emergent trap-like aging behavior in a variety of disordered models. Our numerical results are backed by analytic derivations and heuristic discussions. Such exploration reveals some of the tricks needed to analyze the trap behavior in spite of the occurrence of secondary processes, of the existence of dynamical correlations and of finite system's size effects.Comment: 25 pages, 15 figure

Spontaneous energy-barrier formation in entropy-driven glassy dynamics

The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough potential energy landscape and we analyze it both numerically and analytically. The model provides an example of dynamics where typical relaxation channels go over finite-potential energy barriers despite the presence of less-energy-demanding escaping paths in configurational space; we expect this phenomenon to be also relevant in the thermally activated regime of realistic models of glass-formers. In this case, we found that typical dynamical paths episodically reach an high-fixed-threshold energy, unexpectedly giving rise to a simple thermally activated aging phenomenology. In order to unveil this peculiar aging behavior, we introduce a novel description of the dynamics in terms of spontaneously emerging dynamical basins

Random Pinning Glass Transition: Hallmarks, Mean-Field Theory and Renormalization Group Analysis

We present a detailed analysis of glass transitions induced by pinning particles at random from an equilibrium configuration. We first develop a mean-field analysis based on the study of p-spin spherical disordered models and then obtain the three dimensional critical behavior by the Migdal-Kadanoff real space renormalization group method. We unveil the important physical differences with the case in which particles are pinned from a random (or very high temperature) configuration. We contrast the pinning particles approach to the ones based on biasing dynamical trajectories with respect to their activity and on coupling to equilibrium configurations. Finally, we discuss numerical and experimental tests.Comment: Submitted for publication in J. Chem. Phys. for the special topic issue on the glass transition. 28 Page

First Principle Computation of Random Pinning Glass Transition, Glass Cooperative Length-Scales and Numerical Comparisons

As a guideline for experimental tests of the ideal glass transition (Random Pinning Glass Transition, RPGT) that shall be induced in a system by randomly pinning particles, we performed first-principle computations within the Hypernetted chain approximation and numerical simulations of a Hard Sphere model of glass-former. We obtain confirmation of the expected enhancement of glassy behaviour under the procedure of random pinning, which consists in freezing a fraction $c$ of randomly chosen particles in the positions they have in an equilibrium configuration. We present the analytical phase diagram as a function of $c$ and of the packing fraction $\phi$, showing a line of RPGT ending in a critical point. We also obtain first microscopic results on cooperative length-scales characterizing medium-range amorphous order in Hard Spere glasses and indirect quantitative information on a key thermodynamic quantity defined in proximity of ideal glass transitions, the amorphous surface tension. Finally, we present numerical results of pair correlation functions able to differentiate the liquid and the glass phases, as predicted by the analytic computations.Comment: Working draft, comments are welcom

Dynamical Mean-Field Theory and Aging Dynamics

Dynamical Mean-Field Theory (DMFT) replaces the many-body dynamical problem with one for a single degree of freedom in a thermal bath whose features are determined self-consistently. By focusing on models with soft disordered $p$-spin interactions, we show how to incorporate the mean-field theory of aging within dynamical mean-field theory. We study cases with only one slow time-scale, corresponding statically to the one-step replica symmetry breaking (1RSB) phase, and cases with an infinite number of slow time-scales, corresponding statically to the full replica symmetry breaking (FRSB) phase. For the former, we show that the effective temperature of the slow degrees of freedom is fixed by requiring critical dynamical behavior on short time-scales, i.e. marginality. For the latter, we find that aging on an infinite number of slow time-scales is governed by a stochastic equation where the clock for dynamical evolution is fixed by the change of effective temperature, hence obtaining a dynamical derivation of the stochastic equation at the basis of the FRSB phase. Our results extend the realm of the mean-field theory of aging to all situations where DMFT holds.Comment: 28 pages, 3 figure

Renormalization group analysis of the random first order transition

We consider the approach describing glass formation in liquids as a progressive trapping in an exponentially large number of metastable states. To go beyond the mean-field setting, we provide a real-space renormalization group (RG) analysis of the associated replica free-energy functional. The present approximation yields in finite dimensions an ideal glass transition similar to that found in mean field. However, we find that along the RG flow the properties associated with metastable glassy states, such as the configurational entropy, are only defined up to a characteristic length scale that diverges as one approaches the ideal glass transition. The critical exponents characterizing the vicinity of the transition are the usual ones associated with a first-order discontinuity fixed point.Comment: 5 pages, 3 figure