Size-stretched exponential relaxation in a model with arrested states

2020/04/30 by Vaibhav Gupta, Saroj Kumar Nandi, Mustansir Barma
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Autocorrelation #Chemistry #Correlation function (quantum field theory) #Exponential decay #Exponential function #Function (biology) #Material Dynamics and Properties #Mathematical analysis #Mathematical physics #Mathematics #Physics #Power law #Quantum mechanics #Relaxation (psychology) #Statistical physics #Statistics #Steady state (chemistry) #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.102.022103

published as Phys. Rev. E 102, 022103 (2020) · Final version

openalex publication_date 2020/08/06 · arxiv created 2020/08/08 · arxiv updated 2020/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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