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  • Random walk statistics  (1)
  • queueing process  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Critical dynamics of finite Ising model (1982)
    Springer
    Journal of statistical physics 28 (1982), S. 307-323 
    Details
    ISSN: 1572-9613
    Keywords: Ising ; critical dynamics ; spectral powers ; queueing process
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Glauber kinetics of Ising spins is considered as a queueing process and simulated “event by event” as first proposed by Bortz, Kalos, and Lebowitz. The advantage of this algorithm compared to the standard single-flip Monte Carlo method is discussed for the situation of slowing down of dynamics. This process is used to generate fluctuations of magnetization and energy in the critical regimeT=Tc of two-dimensional Ising models. The analysis of these fluctuations leads to numerical determination of the critical exponents for dynamics: for the size dependence of correlation time atT c , and Μ for frequency dependence of the power spectrumS(ω)~ω −µ . From the finite-size scaling hypothesis, scaling relations are settled which are confirmed by this numerical experiment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01012608
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Random walk statistics on fractal structures (1984)
    Springer
    Journal of statistical physics 36 (1984), S. 547-560 
    Details
    ISSN: 1572-9613
    Keywords: Random walk statistics ; fractal structures ; spectral dimension ; percolation clusters
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider some statistical properties of simple random walks on fractal structures viewed as networks of sites and bonds: range, renewal theory, mean first passage time, etc. Asymptotic behaviors are shown to be controlled by the fractal (¯d) and spectral (¯d) dimensionalities of the considered structure. A simple decimation procedure giving the value of (¯d) is outlined and illustrated in the case of the Sierpinski gaskets. Recent results for the trapping problem, the self-avoiding walk, and the true-self-avoiding walk are briefly reviewed. New numerical results for diffusion on percolation clusters are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01012921
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    Paper (German National Licenses)
    Fulltext
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