Stretched exponential to power-law: crossover of relaxation in a kinetically constrained model

TL;DR

This paper introduces a simple one-dimensional spin model demonstrating a crossover from stretched exponential to power-law relaxation, driven by changing dominant excitations, providing insight into complex relaxation behaviors.

Contribution

It presents a new spin model capturing the crossover from SER to power-law decay, linking excitation dynamics to relaxation patterns in complex systems.

Findings

Relaxation changes from diffusive DWs to doublons over time.

Model reproduces crossover from SER to power-law decay.

Analytic and numerical results support the mechanism.

Abstract

The autocorrelation function in many complex systems shows a crossover in the form of its decay: from stretched exponential relaxation (SER) at short times to power law at long times. Studies of the mechanisms leading to such multiple relaxation patterns are rare. Additionally, the inherent complexity of these systems makes it hard to understand the underlying mechanism leading to the crossover. Here we develop a simple one-dimensional spin model, which we call a Domain Wall (DW) to Doublon model, that shows such a crossover as the nature of the excitations governing the relaxation dynamics changes with temperature and time. The relevant excitations are DWs and bound pairs of DWs, which we term `doublons'. The diffusive motion of the DWs govern the relaxation at short times, whereas the diffusive motion of the doublons yields the long time decay. This change of excitations and their relaxation leads to a crossover from SER to power law in the decay pattern of the autocorrelation function. We augment our numerical results with simple physical arguments and analytic derivations.