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  • 1
    Electronic Resource
    Electronic Resource
    Convergence to Equilibrium of Random Ising Models in the Griffiths Phase (1998)
    Springer
    Journal of statistical physics 92 (1998), S. 337-351 
    Details
    ISSN: 1572-9613
    Keywords: Random spin systems ; diluted Ising model ; Glauber dynamics ; relaxation time ; Griffiths singularities ; FK representation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider Glauber-type dynamics for disordered Ising spin systems with nearest neighbor pair interactions in the Griffiths phase. We prove that in a nontrivial portion of the Griffiths phase the system has exponentially decaying correlations of distant functions with probability exponentially close to 1. This condition has, in turn, been shown elsewhere to imply that the convergence to equilibrium is faster than any stretched exponential, and that the average over the disorder of the time-autocorrelation function goes to equilibrium faster than exp[−k(log t) d/(d−1)]. We then show that for the diluted Ising model these upper bounds are optimal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023077101354
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Some remarks on pathologies of renormalization-group transformations for the Ising model (1993)
    Springer
    Journal of statistical physics 72 (1993), S. 1169-1177 
    Details
    ISSN: 1572-9613
    Keywords: Decimation ; Renormalization-group ; non-Gibbsianness ; Finite-size conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The results recently obtained by van Enter, Fernandez, and Sokal on non-Gibbsianness of the measurev =T b μβ,h arising from the application of a single decimation transformationT b , with spacingb, to the Gibbs measure μβ,h , of the Ising model, for suitably chosen large inverse temperatureβ and nonzero external fieldh, are critically analyzed. In particular, we show that if, keeping fixed the same values ofβ, h, andb, one iterates a sufficiently large number of timesn the transformationT b , one obtains a new measurev ′ = (T b )nμβ,h which is Gibbsian and moreover very weakly coupled.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01048184
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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