TY - JOUR
T1 - Dynamical mean-field theory and aging dynamics
AU - Altieri, Ada
AU - Biroli, Giulio
AU - Cammarota, Chiara
PY - 2020/9/18
Y1 - 2020/9/18
N2 - 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 DMFT. We study cases with only one slow time-scale, corresponding statically to the one-step replica symmetry breaking 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 the 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.
AB - 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 DMFT. We study cases with only one slow time-scale, corresponding statically to the one-step replica symmetry breaking 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 the 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.
KW - Aging dynamics
KW - Disordered systems
KW - Dynamical mean-field formalism
KW - Replica method
UR - http://www.scopus.com/inward/record.url?scp=85090906611&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/aba3dd
DO - 10.1088/1751-8121/aba3dd
M3 - Article
AN - SCOPUS:85090906611
SN - 1751-8113
VL - 53
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 37
M1 - 375006
ER -