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

Authors
  • Mukherjee, Sukanta
  • Pareek, Puneet
  • Barma, Mustansir
  • Kumar Nandi, Saroj
Type
Published Article
Journal
Journal of Statistical Mechanics: Theory and Experiment
Publisher
IOP Publishing
Publication Date
Feb 09, 2024
Volume
2024
Issue
2
Identifiers
DOI: 10.1088/1742-5468/ad1f55
Source
ioppublishing
Keywords
Disciplines
  • Paper section: Classical statistical mechanics, equilibrium and non-equilibrium
License
Unknown

Abstract

The autocorrelation function in many complex systems shows a crossover in the form of its decay: from a stretched exponential relaxation (SER) at short times to a 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 governs 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 a power law in the decay pattern of the autocorrelation function. We augment our numerical results with simple physical arguments and analytic derivations.

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