Stretched-exponential behavior and random walks on diluted hypercubic lattices
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2011-10-18
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Diffusion on a diluted hypercube has been proposed as a model for glassy relaxation and is an example of the more general class of stochastic processes on graphs. In this article we determine numerically through large-scale simulations the eigenvalue spectra for this stochastic process and calculate explicitly the time evolution for the autocorrelation function and for the return probability, all at criticality, with hypercube dimensions N up to N=28. We show that at long times both relaxation functions can be described by stretched exponentials with exponent 1/3 and a characteristic relaxation time which grows exponentially with dimension N. The numerical eigenvalue spectra are consistent with analytic predictions for a generic sparse network model. © 2011 American Physical Society.
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Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 84, n. 4, 2011.