Role of fluctuations in finite-dimensional glassy systems
Friday, the 17th November at 11:00 AM,
room CV002 Uni Carl Vogt
LABORATOIRE DE PHYSIQUE THEORIQUE DE LA MATIERE CONDENSEE
CNRS-UMR 7600, Université Pierre et Marie Curie, Paris, France
When the temperature diminishes, glassy systems present a very sluggish dynamics and at low enough temperature can finish in some arrested state. Even if this arrested state is dynamically frozen, it does not show any sign of conventional long-range order and structurally looks disordered.
In this seminar I will talk about the case of structural glasses, to which category supercooled liquids belong to, and spin glasses. For the former, the observation of a huge slowing down of the relaxation time when the temperature decreases has not found a consensual explanation and is sometimes associated to the existence of an underlying thermodynamic transition or of an underlying dynamical transition. For the latter, the existence of a finite-temperature thermodynamic transition when no external field is applied is well established, but the nature of the "spin-glass" phase thus reached and the existence of an in-field transition are open questions.
Since the mean-field approximations (that neglect spatial fluctuations) can be informative for finite-dimensional systems, I will begin by presenting the mean-field theories that exist for structural and spin glasses. They are intricate theories whose scenarios can be fragile to the introduction of fluctuations that are present in finite-dimensional systems. Since the study of the effect of fluctuations directly within the formalism of these rather complicate theories is a daunting task, I will present two simpler problems in which the effect of fluctuations can be thoroughly investigated.
For the case of structural glasses, I will present a glass-former model called the "plaquette-spin" model. I will investigate thermodynamic properties of the system studied on different lattice topologies (Bethe vs. Euclidean lattices) allowing for a distinction between "short-range" and "long-range" fluctuations. For the case of spin glasses, I will study the critical properties of the Ising spin glass in zero applied field by means of the so-called "nonperturbative renormalization group" method that allows for a progressive account of fluctuations of longer ranges. This study is a primary step to try to construct a predictive approximation scheme for the nonperturbative renormalization group and the next step would be to apply it to the study of the nature of the spin-glass phase.