Confinement as a tool to probe amorphous order

We study the effect of confinement on glassy liquids using Random First Order Transition theory as framework. We show that the characteristic length-scale above which confinement effects become negligible is related to the point-to-set length-scale introduced to measure the spatial extent of amorphous order in super-cooled liquids. By confining below this characteristic size, the system becomes a glass. Eventually, for very small sizes, the effect of the boundary is so strong that any collective glassy behavior is wiped out. We clarify similarities and differences between the physical behaviors induced by confinement and by pinning particles outside a spherical cavity (the protocol introduced to measure the point-to-set length). Finally, we discuss possible numerical and experimental tests of our predictions.Comment: 5 pages, 3 figures and EPAPS (4 pages, 1 figure

Glassy dynamics of partially pinned fluids: an alternative mode-coupling approach

We use a simple mode-coupling approach to investigate glassy dynamics of partially pinned fluid systems. Our approach is different from the mode-coupling theory developed by Krakoviack [Phys. Rev. Lett. 94, 065703 (2005), Phys. Rev. E 84, 050501(R) (2011)]. In contrast to Krakoviack's theory, our approach predicts a random pinning glass transition scenario that is qualitatively the same as the scenario obtained using a mean-field analysis of the spherical p-spin model and a mean-field version of the random first-order transition theory. We use our approach to calculate quantities which are often considered to be indicators of growing dynamic correlations and static point-to-set correlations. We find that the so-called static overlap is dominated by the simple, low pinning fraction contribution. Thus, at least for randomly pinned fluid systems, only a careful quantitative analysis of simulation results can reveal genuine, many-body point-to-set correlations

Ideal Glass Transitions by Random Pinning

We study the effect of freezing the positions of a fraction $c$ of particles from an equilibrium configuration of a supercooled liquid at a temperature $T$. We show that within the Random First-Order Transition theory pinning particles leads to an ideal glass transition for a critical fraction $c=c_{K}(T)$ even for moderate super-cooling, e.g. close to the Mode-Coupling transition temperature. We first derive the phase diagram in the $T-c$ plane by mean field approximations. Then, by applying a real-space renormalization group method, we obtain the critical properties for $|c-c_{K}(T)|\rightarrow 0$, in particular the divergence of length and time scales. These are dominated by two zero-temperature fixed points. We also show that for $c=c_{K}(T)$ the typical distance between frozen particles is related to the static point-to-set lengthscale of the unconstrained liquid. We discuss what are the main differences when particles are frozen in other geometries and not from an equilibrium configuration. Finally, we explain why the glass transition induced by freezing particles provides a new and very promising avenue of research to probe the glassy state and ascertain, or disprove, the validity of the theories of the glass transition.Comment: 6 pages, 3 figures Revised version with new references and discussion

A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first-order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e. at coexistence, where the critical nucleus becomes infinitely large.Comment: 12 pages, 15 figure

Complexity of energy barriers in mean-field glassy systems

We analyze the energy barriers that allow escapes from a given local minimum in a complex high-dimensional landscape. We perform this study by using the Kac-Rice method and computing the typical number of critical points of the energy function at a given distance from the minimum. We analyze their Hessian in terms of random matrix theory and show that for a certain regime of energies and distances critical points are index-one saddles, or transition states, and are associated to barriers. We find that the transition state of lowest energy, important for the activated dynamics at low temperature, is strictly below the "threshold" level above which saddles proliferate. We characterize how the quenched complexity of transition states, important for the activated processes at finite temperature, depends on the energy of the state, the energy of the initial minimum, and the distance between them. The overall picture gained from this study is expected to hold generically for mean-field models of the glass transition

Opinion dynamics with emergent collective memory: A society shaped by its own past

In order to understand the development of common orientation of opinions in the modern world we propose a model of a society described as a large collection of agents that exchange their expressed opinions under the influence of their mutual interactions and external events. In particular we introduce an interaction bias which results in the emergence of a collective memory such that the society is able to store and recall information coming from several external signals. Our model shows how the inner structure of the society and its future reactions are shaped by its own history. We provide an analytical explanation of such mechanism and we study the features of external influences with higher impact on the society. We show the emergent similarity between the reaction of a society modelled in this way and the Hopfield-like mechanism of information retrieval in Neural Networks

Dynamical Instantons and Activated Processes in Mean-Field Glass Models

We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical $p$-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.Comment: v3, conclusions extended and minor revision