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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
    On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point (1996)
    Springer
    Journal of statistical physics 85 (1996), S. 55-102 
    Details
    ISSN: 1572-9613
    Keywords: Stochastic Ising model ; phase coexistence ; relaxation time ; spectral gap ; surface tension ; large deviations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider the two-dimensional stochastic Ising model in finite square Λ with free boundary conditions, at inverse temperature β〉β0 and zero external field. Using duality and recent results of Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli in the low-temperature regime to any temperature below the critical one. In particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of Λ, with a rate constant determined by the surface tension along one of the coordinate axes. We also extend to the same range of temperatures the result due to Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02175556
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    Paper (German National Licenses)
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