TY - JOUR
T1 - Following the evolution of glassy states under external perturbations
T2 - the full replica symmetry breaking solution
AU - Haeupler, Bernhard
AU - Pandurangan, Gopal
AU - Peleg, David
AU - Rajaraman, Rajmohan
AU - Sun, Zhifeng
N1 - European Research Council under the European Union [247328]; Weizmann Institute of Science; ERC grant NPRGGLASS
PY - 2016/5
Y1 - 2016/5
N2 - The state-following technique allows the study of metastable glassy states under external perturbations. Here we show how this construction can be used to study the behavior of glassy states of Hard Spheres in infinite dimensions under compression or shear strain. In Rainone et al (2015 Phys. Rev. Lett. 114 015701) it has been shown that in both cases, when the external perturbation is sufficiently strong, glassy states undergo a second-order transition, called the Gardner transition, whereupon a hierarchical structure of marginal micro-states manifests within the original glass state. The purpose of this work is to study the solution of the state-following construction in this marginal phase. We show that upon compression, close to the jamming transition, the metastable states are described by a scaling solution characterized by a set of non-trivial critical exponents that agree with the results of Charbonneau et al (2014 Nat. Commun. 5 3725), and we compute the value of the jamming density phi(j) for various glassy states. Moreover we show that under the action of the shear strain, beyond the Gardner point, the metastable states can be followed in the marginal phase and we detect an overshoot in the stress-strain curve in agreement with numerical and experimental observations. Finally we further characterize the Gardner transition point by computing both the chi(4) susceptibility and the exponent parameter lambda that characterize the critical slowing down of the dynamics within a glassy state close to the transition.
AB - The state-following technique allows the study of metastable glassy states under external perturbations. Here we show how this construction can be used to study the behavior of glassy states of Hard Spheres in infinite dimensions under compression or shear strain. In Rainone et al (2015 Phys. Rev. Lett. 114 015701) it has been shown that in both cases, when the external perturbation is sufficiently strong, glassy states undergo a second-order transition, called the Gardner transition, whereupon a hierarchical structure of marginal micro-states manifests within the original glass state. The purpose of this work is to study the solution of the state-following construction in this marginal phase. We show that upon compression, close to the jamming transition, the metastable states are described by a scaling solution characterized by a set of non-trivial critical exponents that agree with the results of Charbonneau et al (2014 Nat. Commun. 5 3725), and we compute the value of the jamming density phi(j) for various glassy states. Moreover we show that under the action of the shear strain, beyond the Gardner point, the metastable states can be followed in the marginal phase and we detect an overshoot in the stress-strain curve in agreement with numerical and experimental observations. Finally we further characterize the Gardner transition point by computing both the chi(4) susceptibility and the exponent parameter lambda that characterize the critical slowing down of the dynamics within a glassy state close to the transition.
U2 - https://doi.org/10.1088/1742-5468/2016/05/053302
DO - https://doi.org/10.1088/1742-5468/2016/05/053302
M3 - مقالة
SN - 1742-5468
VL - 2016
JO - Journal Of Statistical Mechanics-Theory And Experiment
JF - Journal Of Statistical Mechanics-Theory And Experiment
IS - 5
M1 - 53302
ER -