Random walks in a simple percolation model with two jump frequencies |
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Affiliation: | 1. School of Materials Science and Engineering, Jiangsu University, Zhenjiang, 212013, Jiangsu, China;2. School of Materials Science and Engineering, Tsinghua University, Haidian District, 100084, Beijing, China |
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Abstract: | We consider transport properties of the system in which the good-conducting bonds lie in parallel planes linked by poor-conducting bonds and the concentration p of good-conducting bonds is close to the two-dimensional percolation threshold pc. The diffusion coefficient D(τ) which describes the random walking in directions along the planes is calculated as a function of variable τ = p − pc. For τ → 0 the asymptotic relation D(τ)/D(0) − 1 | ∼ |τ|α is found w α = 2ν − s. Here s is the superconductivity exponent and ν is the correlation length exponent. It is argued that such behavior is to be expected also for more general models. |
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