Glassy behaviour in disordered systems with non-relaxational dynamics

TL;DR

This paper demonstrates that certain disordered systems with non-relaxational dynamics can exhibit glassy behavior at nonzero temperatures, which can be understood through a proper interpretation of mean-field theory, revealing complex dynamical regimes.

Contribution

It reveals that glassy behavior can occur in non-relaxational disordered systems and clarifies its origins within mean-field theory, challenging previous assumptions.

Findings

Disordered systems with non-relaxational dynamics show glassy behavior at finite temperatures.

Finite systems display self-similar dynamics with alternating fast motion and trapping.

Mean-field theory, when properly interpreted, explains the roots of this glassy behavior.

Abstract

We show that a family of disordered systems with non-relaxational dynamics may exhibit ``glassy'' behavior at nonzero temperature, although such a behavior appears to be ruled out by a face-value application of mean-field theory. Nevertheless, the roots of this behavior can be understood within mean-field theory itself, properly interpreted. Finite systems belonging to this family have a dynamical regime with a self-similar pattern of alternating periods of fast motion and trapping.