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  • 1
    Electronic Resource
    Electronic Resource
    On the Swendsen-Wang dynamics. I. Exponential convergence to equilibrium (1991)
    Springer
    Journal of statistical physics 62 (1991), S. 117-133 
    Details
    ISSN: 1572-9613
    Keywords: Monte Carlo algorithms ; Ising model ; approach to equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present rigorous results on the exponential convergence to equilibrium for the Swendsen-Wang stochastic dynamics for thed-dimensional Ising ferromagnet with external magnetic fieldh in the thermodynamic limit. We consider various situations, mainly in the low-temperature regime, in which boundary conditions are homogeneous and parallel or opposite to the external field. In the latter case we relate directly the tunneling from the metastable phase to the stable one with the exponential convergence to equilibrium.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020862
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  • 2
    Electronic Resource
    Electronic Resource
    On the Swendsen-Wang dynamics. II. Critical droplets and homogeneous nucleation at low temperature for the two-dimensional Ising model (1991)
    Springer
    Journal of statistical physics 62 (1991), S. 135-159 
    Details
    ISSN: 1572-9613
    Keywords: Ising model ; random cluster dynamics ; stable and metastable phases ; nucleation ; critical droplets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider the Swendsen-Wang dynamics for the two-dimensional Ising model at low temperature in the presence of a small negative magnetic fieldh and with plus boundary conditions at the boundary of an arbitrarily large square. We analyze in detail the tunneling from the metastable phase to the stable one. In particular, we obtain an upper bound on the tunneling timet β by explicitly constructing paths in the space of spin configurations that drive the system from the metastable phase to the stable one. In our analysis the transition takes place through the formation of droplets of the right phase inside the wrong one with side greater than a certain critical valuel c . The values of the tunneling time and ofl c coincide with those found for a single-spin-flip dynamics in finite volume by Jordao-Neves and Schonmann.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020863
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  • 3
    Electronic Resource
    Electronic Resource
    Metastability and exponential approach to equilibrium for low-temperature stochastic Ising models (1990)
    Springer
    Journal of statistical physics 61 (1990), S. 1105-1119 
    Details
    ISSN: 1572-9613
    Keywords: Ising model ; Glauber dynamics ; metastability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a proof of the exponential convergence to equilibrium of single-spin-flip stochastic dynamics for the two-dimensional Ising ferromagnet in the low-temperature case with not too small external magnetic fieldh uniformly in the volume and in the boundary conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01014367
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  • 4
    Electronic Resource
    Electronic Resource
    Renormalization group for Markov chains and application to metastability (1993)
    Springer
    Journal of statistical physics 73 (1993), S. 83-121 
    Details
    ISSN: 1572-9613
    Keywords: Markov chains ; renormalization group ; metastability ; Ising model ; Monte Carlo dynamical simulations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameterβ. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01052752
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