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  • 1
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Stochastic Ising model ; phase coexistence ; relaxation time ; spectral gap ; surface tension ; large deviations
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02175556
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  • 2
    Digitale Medien
    Digitale Medien
    The Spectral Gap for the Kawasaki Dynamics at Low Temperature (1999)
    Springer
    Journal of statistical physics 95 (1999), S. 215-271 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Kawasaki dynamics ; spectral gap ; large deviations ; Wulff construction
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract In this paper we analyze the convergence to equilibrium of Kawasaki dynamics for the Ising model in the phase coexistence region. First we show, in strict analogy with the nonconservative case, that in any lattice dimension, for any boundary condition and any positive temperature and particle density, the spectral gap in a box of side L does not shrink faster than a negative exponential of the surface L d−1. Then we prove that, in two dimensions and for free boundary condition, the spectral gap in a box of side L is smaller than a negative exponential of L provided that the temperature is below the critical one and the particle density ρ satisfies ρ∈(ρ*−, ρ*+), where ρ*± represents the particle density of the plus and minus phase, respectively.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004581512343
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