Molecular trajectory algorithm for random walks on percolation systems at criticality in two and three dimensions

Wei Cen, Dongbing Liu and Bingquan Mao

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 4, 925-929

Abstract: Random walk simulations based on a molecular trajectory algorithm are performed on critical percolation clusters. The analysis of corrections to scaling is carried out. It has been found that the fractal dimension of the random walk on the incipient infinite cluster is dw=2.873±0.008 in two dimensions and 3.78 ± 0.02 in three dimensions. If instead the diffusion is averaged over all clusters at the threshold not subject to the infinite restriction, the corresponding critical exponent k is found to be k=0.3307±0.0014 for two-dimensional space and 0.199 ± 0.002 for three-dimensional space. Moreover, in our simulations the asymptotic behaviors of local critical exponents are reached much earlier than in other numerical methods.

Keywords: Percolation; Molecular trajectory algorithm; Alexander–Orbach conjecture; Monte Carlo simulation; Diffusion; Critical exponents (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:4:p:925-929

DOI: 10.1016/j.physa.2011.01.003

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