Size-stretched exponential relaxation in a model with arrested states
We study the effect of a rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. Explicitly, we find that the spatial correlation function decays as exp(-2r/sqrt[L]) as a function of spatial separation r in a system with L sites in the steady state, while the temporal autocorrelation function follows exp[-(t/τ_{L})^{1/2}], where t is the time and τ_{L} proportional to L. In the coarsening regime, after time t_{w}, there are two growing length scales, namely L(t_{w})∼t_{w}^{1/2} and R(t_{w})∼t_{w}^{1/4}; the spatial correlation function decays as exp[-r/R(t_{w})]. Interestingly, the stretched exponential form of the autocorrelation function of a single typical sample in the steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power-law decay at large times.
| Medienart: |
E-Artikel |
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| Erscheinungsjahr: |
2020 |
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| Erschienen: |
2020 |
| Enthalten in: |
Zur Gesamtaufnahme - volume:102 |
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| Enthalten in: |
Physical review. E - 102(2020), 2-1 vom: 17. Aug., Seite 022103 |
| Sprache: |
Englisch |
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| Beteiligte Personen: |
Gupta, Vaibhav [VerfasserIn] |
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| Anmerkungen: |
Date Revised 18.09.2020 published: Print Citation Status PubMed-not-MEDLINE |
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| doi: |
10.1103/PhysRevE.102.022103 |
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| funding: |
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| Förderinstitution / Projekttitel: |
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| PPN (Katalog-ID): |
NLM315139250 |
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| 245 | 1 | 0 | |a Size-stretched exponential relaxation in a model with arrested states |
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| 500 | |a Date Revised 18.09.2020 | ||
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| 500 | |a Citation Status PubMed-not-MEDLINE | ||
| 520 | |a We study the effect of a rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. Explicitly, we find that the spatial correlation function decays as exp(-2r/sqrt[L]) as a function of spatial separation r in a system with L sites in the steady state, while the temporal autocorrelation function follows exp[-(t/τ_{L})^{1/2}], where t is the time and τ_{L} proportional to L. In the coarsening regime, after time t_{w}, there are two growing length scales, namely L(t_{w})∼t_{w}^{1/2} and R(t_{w})∼t_{w}^{1/4}; the spatial correlation function decays as exp[-r/R(t_{w})]. Interestingly, the stretched exponential form of the autocorrelation function of a single typical sample in the steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power-law decay at large times | ||
| 650 | 4 | |a Journal Article | |
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| 700 | 1 | |a Barma, Mustansir |e verfasserin |4 aut | |
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